how does one apply this penalty to the character sheet in DnD Beyond ? ? ? 

I created a custom magic item that applies a -1 penalty to all applicable areas. You can add four of them, equip them, then remove one from your inventory after each long rest.

https://www.dndbeyond.com/magic-items/312656-cursed-soul-fragment

Quote from WildGrue >>

I created a custom magic item that applies a -1 penalty to all applicable areas. You can add four of them, equip them, then remove one from your inventory after each long rest.

https://www.dndbeyond.com/magic-items/312656-cursed-soul-fragment

Well played!!

This is not a spell that is possible for a wizard to learn unless they have multiclassed into a caster like a cleric or bard. So no they could not add this to their spell book.

False, actually. One of the more nonconventional uses of wish is "I wish to add (non wizard spell) to my spell list permanently." Depending on the DM, there might be a bit of unintended consequences, but hey, keep me alive and supply me with diamonds, and I can make sure it doesn't kill you. At least, permanently.

Why does an LG class (paladin) use a necromancy spell?

While necromancy is often associated with evil or dark magic, it usually isn't.  I don't have the exact definition of the word, but necromancy is magic that usually has something to do with the dead.  Raise Dead is a spell that, obviously, is about the dead.  Just as Raise Undead does.  Both have different effects, but are within the same school.  Nearly all healing spells are classed under the school of necromancy.

Regarding evil, I think what's evil depends on how the spell is used.  For example, a cleric knows the spell Animate Dead, which basically makes puppets out of corpses to fight for you.  If the cleric worships a good-aligned god, then this spell probably doesn't cross the line because it's not bringing back someone's spirit or soul to do your bidding.  It's "tool-use", to put it lightly.  However, it would be considered evil if the cleric uses the undead minions to slaughter a village.  Or if they use Resurrection to bring back Karthog, Destroyer of Worlds.

Paladin isn't a LG class. There are no alignment restrictions in 5e for Paladin.

Quote from Flint_Ironfist9 >>

Why does an LG class (paladin) use a necromancy spell?

 

 Because the necromancy spells in question are Revivify (a form of resurrection) and Raise Dead (a form of resurrection), which have the general purpose of helping your teammates and/or the common people. Helping others is basically what a paladin does on the regular, both in terms of role-playing and of combat, and these spells work toward that end (and even if you're playing an oathbreaker or oath of conquest, your character might want to bring their best minions back from the dead from time to time). Besides, the necromancy school of magic is no more evil than, say, enchantment or evocation (particularly since spells and classes can't have alignments in 5e)

Quote from Flint_Ironfist9 >>

Why does an LG class (paladin) use a necromancy spell?

 

 From my understanding, the school of necromancy has less to do with evil and raising zombies and the such and more to do with manipulating people's life forces in general such as healing them, bringing them back from the dead, or plain old drain their life itself, and as others have already said, there are no alignment restrictions for classes.

Question: Can raise dead be used on a corpse that had people mended body parts back on? So lets say a hand was cut off and the player dies. Party decides to use mending to attach the hand. Then tries to use raise dead since they aren't high enough level to use resurrection.

Since I figured there are spells that bring them back with body parts. This would only bring them back with a crippled hand (no use of movement and no feeling). Wanted a second opinion though.

It doesn't make sense that a person can be repaired while dead but not while alive, so I'd say that mending just isn't meant to repair such complicated breaks. It doesn't specify in the spell but the examples given are extremely simple like a year in a wineskin or a broken key.

Mending specifically repairs an Object. It does not repair a Creature. Even if said creature is dead, it is still considered a Creature.

Since the creature is dead. Corpses are specified as objects in 5th edition. Thus using mending to repair it. Thus becoming a problem.

Man, I've been trying to explain to my party/group that a paladin doesn't have be all law abiding and generally good. All a paladin has to do is stay true to his oath, which can be pretty much anything depending on the subclass.

Fun fact, it won't help you if you get your brain eaten by an intellect devourer.

Thank you, This was very helpful during my current campaign

I’d rule that if the missing part is present when Raise Dead is used, it would be mended. It says “doesn’t replace missing body parts”, with “missing” being the key. It isn’t missing if it’s with the rest of the corpse, merely detached...

If one were disemboweled, the fact that your innards were lying on the floor wouldn’t prevent your being raised, would it? Or would your allies first need to stuff your gizzards back into your torso and hope they didn’t miss your liver or something? 
:-D

But as with the ‘Wish’ spell the DM could have some fun with that as well...    “You successfully raise <rogue’s name> from the dead.  He may regret his return to the living however, as his recently severed hand is now unfortunately, grotesquely, backwards. On the up-side, it will take some time to adjust before he’ll be able to stick his dagger in your back’s!”

What about replacing the -4 penalty with fatigue levels ?

- Coming back from the dead is an ordeal. The target takes 4 levels of fatigue. Every time the target finishes a long rest, 1 level of fatigue is restored.

Why do police use guns?  Tools aren't evil.  Evil people using tools for evil are evil.  Necromancy isn't inherently evil.