So I wanted to take a crack at changing the sorcerer a bit without going to overboard with it. So, here it is. 

The Sorcerer Table

Class Features

As a sorcerer, you gain the following class features.

Hit Points

Hit Dice: 1d8 per sorcerer level
Hit Points at 1st Level: 8 + your Constitution modifier
Hit Points at Higher Levels: 1d8 (or 5) + your Constitution modifier per sorcerer level after 1st

Proficiencies

Armor: Light armor
Weapons: Daggers, darts, slings, quarterstaffs, light crossbows
Tools: None
Saving Throws: Constitution, Charisma
Skills: Choose two from Arcana, Deception, Insight, Intimidation, Persuasion, and Religion

Equipment

You start with the following equipment, in addition to the equipment granted by your background:

• (a) a light crossbow and 20 bolts or (b) any simple weapon
• (a) a component pouch or (b) an arcane focus
• (a) a dungeoneer’s pack or (b) an explorer’s pack
• Leather armor and two daggers

Spellcasting

An event in your past, or in the life of a parent or ancestor, left an indelible mark on you, infusing you with arcane magic. This font of magic, whatever its origin, fuels your spells. See Spells Rules for the general rules of spellcasting and the Spells Listing for the sorcerer spell list.

Cantrips

At 1st level, you know four cantrips of your choice from the sorcerer spell list. You learn additional sorcerer cantrips of your choice at higher levels, as shown in the Cantrips Known column of the Sorcerer table.

Spell Slots

The Sorcerer table shows how many spell slots you have to cast your sorcerer spells of 1st level and higher. To cast one of these sorcerer spells, you must expend a slot of the spell’s level or higher. You regain all expended spell slots when you finish a long rest.

For example, if you know the 1st-level spell burning hands and have a 1st-level and a 2nd-level spell slot available, you can cast burning hands using either slot.

Spells Known of 1st Level and Higher

You know two 1st-level spells of your choice from the sorcerer spell list.

The Spells Known column of the Sorcerer table shows when you learn more sorcerer spells of your choice. Each of these spells must be of a level for which you have spell slots. For instance, when you reach 3rd level in this class, you can learn one new spell of 1st or 2nd level.

Additionally, when you gain a level in this class, you can choose one of the sorcerer spells you know and replace it with another spell from the sorcerer spell list, which also must be of a level for which you have spell slots.

Spellcasting Ability

Charisma is your spellcasting ability for your sorcerer spells, since the power of your magic relies on your ability to project your will into the world. You use your Charisma whenever a spell refers to your spellcasting ability. In addition, you use your Charisma modifier when setting the saving throw DC for a sorcerer spell you cast and when making an attack roll with one.

Spell save DC = 8 + your proficiency bonus + your Charisma modifier

Spell attack modifier = your proficiency bonus + your Charisma modifier

Spellcasting Focus

You can use an arcane focus (see the Adventuring Gear section) as a spellcasting focus for your sorcerer spells.

Sorcerous Origin

Choose a sorcerous origin, which describes the source of your innate magical power: Draconic Bloodline, detailed at the end of the class description, or one from another source.

Your choice grants you features when you choose it at 1st level and again at 6th, 14th, and 18th level.

Font of Magic

At 2nd level, you tap into a deep wellspring of magic within yourself. This wellspring is represented by sorcery points, which allow you to create a variety of magical effects.

Sorcery Points

You have 3 sorcery points, and you gain more as you reach higher levels, as shown in the Sorcery Points column of the Sorcerer table. You can never have more sorcery points than shown on the table for your level. You regain all spent sorcery points when you finish a long rest.

Flexible Casting

You can use your sorcery points to gain additional spell slots, or sacrifice spell slots to gain additional sorcery points. You learn other ways to use your sorcery points as you reach higher levels.

Creating Spell Slots. You can transform unexpended sorcery points into one spell slot as a bonus action on your turn. The Creating Spell Slots table shows the cost of creating a spell slot of a given level. You can create spell slots no higher in level than 5th.

Any spell slot you create with this feature vanishes when you finish a long rest.

Creating Spell Slots

Converting a Spell Slot to Sorcery Points. As a bonus action on your turn, you can expend one spell slot and gain a number of sorcery points equal to the slot’s level.

Sorcerous Restoration. You have learned to regain some of your sorcerous power. Once per day when you finish a short rest, you can recover sorcery points equal to or less than half your sorcerer level (rounded up).

Metamagic

At 3rd level, you gain the ability to twist your spells to suit your needs. You gain two of the following Metamagic options of your choice. You gain another one at 10th and 17th level.

You can use only one Metamagic option on a spell when you cast it, unless otherwise noted.

Careful Spell

When you cast a spell that forces other creatures to make a saving throw, you can protect some of those creatures from the spell’s full force. To do so, you spend 1 sorcery point and choose a number of those creatures up to your Charisma modifier (minimum of one creature). A chosen creature automatically succeeds on its saving throw against the spell, and they take no damage if they would normally take half damage on a successful save.

Distant Spell

When you cast a spell that has a range of 5 feet or greater, you can spend 1 sorcery point to double the range of the spell.

When you cast a spell that has a range of touch, you can spend 1 sorcery point to make the range of the spell 30 feet.

Empowered Spell

When you roll damage for a spell, you can spend 1 sorcery point to reroll a number of the damage dice up to your Charisma modifier (minimum of one). You must use the new rolls.

You can use Empowered Spell even if you have already used a different Metamagic option during the casting of the spell.

Extended Spell

When you cast a spell that has a duration of 1 minute or longer, you can spend 1 sorcery point to double its duration. You may use more then 1 sorcery point to double the duration of a spell exponentially (ie. 1 hour spell duration would increase to 2 hours with 1 sorcery point, 4 hours with 2 sorcery points, 8 hours with 3 sorcery points, etc), to a maximum duration of 24 hours.

Heightened Spell

When you cast a spell that forces a creature to make a saving throw to resist its effects, you can spend 3 sorcery points to give one target of the spell disadvantage on its first saving throw made against the spell.

Quickened Spell

When you cast a spell that has a casting time of 1 action, you can spend 2 sorcery points to change the casting time to 1 bonus action for this casting.

Subtle Spell

When you cast a spell, you can spend 1 sorcery point to cast it without any somatic or verbal components.

Twinned Spell

When you cast a spell that targets only one creature and doesn’t have a range of self, you can spend a number of sorcery points equal to the spell’s level to target a second creature in range with the same spell (1 sorcery point if the spell is a cantrip).

To be eligible, a spell must be incapable of targeting more than one creature at the spell’s current level. For example, magic missile and scorching ray aren’t eligible, but ray of frost and chromatic orb are.

Seeking Spell (Optional option from Tasha's)

If you make an attack roll for a spell and miss, you can spend 2 sorcery points to reroll the d20, and you must use the new roll.

You can use Seeking Spell even if you have already used a different Metamagic option during the casting of the spell.

Transmuted Spell (Optional option from Tasha's)

When you cast a spell that deals a type of damage from the following list, you can spend 1 sorcery point to change that damage type to one another damage type.

Ability Score Improvement

When you reach 4th level, and again at 8th, 12th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two ability scores of your choice by 1. As normal, you can’t increase an ability score above 20 using this feature.

Using the optional feats rule, you can forgo taking this feature to take a feat of your choice instead.

Sorcerous Versatility (Optional option from Tasha's)

Starting at 4th level, whenever you reach a level in this class that grants the Ability Score Improvement feature, you can do one of the following, representing the magic within you flowing in new ways:

• Replace one of the options you chose for the Metamagic feature with a different Metamagic option available to you.
• Replace one cantrip you learned from this class's Spellcasting feature with another cantrip from the sorcerer spell list.

Magical Guidance (Optional option from Tasha's)

Starting at 5th level, you can tap into your inner wellspring of magic to try to conjure success from failure. When you make an ability check that fails, you can spend 1 sorcery point to reroll the d20, and you must use the new roll, potentially turning the failure into a success.

Level 20 capstone (I'm still figuring out what I want to do here)

Sorry if the formatting is a little wonky, hopefully its understandable. So what do you guys think? Also any suggestions on a level 20 capstone? I'm also planning on adding more spells to the Sorcerer spell list.

Here is my pick for what spells should be added to the revised Sorcerer spell list.

1st Level

Create or Destroy Water

Faerie Fire

Find Familiar

Frost Fingers

Longstrider

Protection from Evil and Good

2nd Level

Continual Flame

Heat Metal

Melf's Acid Arrow

3rd Level

Call Lightning

Life Transference

Spirit Shroud

Wall of Sand

Wind Wall

4th Level

Control Water

Stone Shape

5th Level

Destructive Wave

Maelstrom

Transmute Rock

Wall of Force

6th Level

Otiluke's Freezing Sphere

Primordial Ward

Wall of Ice

Wind Walk

7th Level

Project Image

Regenerate

8th Level

Control Weather

Illusory Dragon

Maddening Darkness

Telepathy

Tsunami

9th Level

Foresight

Invulnerability

Prismatic Wall

Shapechange

Storm of Vengeance

True Polymorph

Okay, I have a few thoughts. 

First, I am curious as to why you gave them a d8 hit dice. I understand wanting to make them a bit more capable at surviving than Wizards, but as they focus a more on Con than Wizards, I don't think that needs any changing. 

Second, I have always thought that Sorcerers should use Constitution as their spellcasting ability instead of Charisma. Their magic comes from their bloodline, lore-wise it doesn't really make sense for them to focus on Charisma. I would keep the skill and saving throw proficiencies the same, though. 

Third, you gave them a lot more sorcery points than before, basically an amount each long rest equal to twice their sorcerer level, due to Sorcerous Restoration and you giving them sorcery points equal to 1.5 times their level. I do like that they get more sorcery points, but it may be too many. If a level 20 sorcerer has the Metamagic Adept feat, each long rest they will have 42 sorcery points. That's a lot, especially with subclass features that take sorcery points to use. 

For example: without this change, a level 20 Clockwork Sorcerer can use their subclass's capstone ability only 3 times each long rest, which takes all but one of their sorcery points. With this change, they can use it 6 times each long rest, which takes all of their sorcery points. Each long rest that's 600 points of healing divided amongst all creatures of your choice within a 30 foot cube of you, along with 6 times of ending every 6th-level spell or lower, and also 6 times of perfect healing on objects in this range. That's . . a lot. I don't know if it's OP, but it feels like the game designers didn't intend for this feature to be able to be used this often. 

I would keep Sorcerous Restoration, probably increase it to an amount of sorcery points equal to half their sorcerer level + their Constitution modifier (rounded up), and then drop the extra base sorcery points. At level 2, that would effectively give them 6 sorcery points (assuming a CON of 16), compared to your 4, which would scale to 35 at level 20, compared to your 4. It starts out a bit more than your version, but eventually has quite a bit less. 

Fourth, I like most of the changes to the Metamagics you did, but am surprised that you didn't make more Metamagic option or give them more Metamagic known. Every sorcerer I have played with has complained about not being able to learn another metamagic until they reach level 10 (yes, the Metamagic Adept feat does exist now, but it's not enough, IMO). Sorcerers have a lot of waiting to do in their class, from the level 6 to level 14 gap in their subclass features, to their gap of features from level 3 to level 20. I would be a bit nicer to them and give them an extra Metamagic known every time they reach a Sorcerer level that grants them an ASI. That will give them a total of 7 metamagic known at level 19, much better than the previous 4. 

Fifth, I would either make them use Spell Points as a base, or at least give it to them as a Class Feature Variant. Combined with my recommendation for the sorcerous restoration, this would solve the issue of not having enough sorcery points, as you can just use the Spell Points in place of the sorcery points. 

Sixth, I would have the Capstone feature give them the ability to know all Metamagic options at once. This is simple and sweet, making them be much more versatile. 

I hope this helps! 

will point out that the classical capstone is very fun becuase there is no limit to how many times you can gain its benefits between long rests, so by spending weeks and weeks and weeks of doing northing but short rests never sleeping even once you can slowly accumulate a lot of 5th level spell slots over time to use in a single adventure.

Also continual flame is not a good fit for the sorcerer, it is hella expensive to cast and you will not want to cast it often since it gets permanent, might be weird

Also does not feel right for the sorcerer to have light armor proficiency, given how it has nothing to do with what they do and what they are supposed to be good at