So, would you use a STR/DEX roll to land this attack, or would it still be your spell modifier?

This is a melee spell attack. If you look under ATTACK/SAVE above the description of a spell, you will see what kind of attack it is.

This would use your spell attack modifier to connect, at melee range, against the target’s AC.

May the Shocking Grasp be delivered through an iron weapon?

If I cast the spell, then I take my sword and I hit the enemy is the shocking grasp delivered?

Quote from IlCaso >>

May the Shocking Grasp be delivered through an iron weapon?

If I cast the spell, then I take my sword and I hit the enemy is the shocking grasp delivered?

 Do you have a rubber handle? XD

Quote from IlCaso >>

May the Shocking Grasp be delivered through an iron weapon?

If I cast the spell, then I take my sword and I hit the enemy is the shocking grasp delivered?

Well, Shocking Grasp has a casting time of 1 Action, and swinging a sword at your enemy constitutes taking the Attack Action, so you definitely could not do both of those simultaneously (even if you were a Fighter with Action Surge - and had access to Shocking Grasp from, say, the Magic Initiate feat, multiclassing, or the Eldritch Knight subclass - the two Actions would occur one after another, not simultaneously). If you tried this, I think it would not be unreasonable of your DM to say "You have successfully shocked your sword. Would you like to do anything with your Bonus Action?"

Do you add your spell-casting modifier to cast this??

can I cast this through leather gloves?

Why does no one understand?! This, to hit, is [roll] + [proficiency] + [spellcasting modifier].

You said, "Why does no one understand?! This, to hit, is [roll] + [proficiency] + [spellcasting modifier]."

Your spellcasting modifier already has your proficiency bonus in it.  "Spell attack modifier = your proficiency bonus + your Intelligence modifier"

So it is {roll} + { spell attack modifier}.

Yes, I was explaining spell attacks because so many people were asking about them.

A good spell for any melee caster

Your spellcasting modifier does not have proficiency. just your spellcasting modifier.

Spell attack modifier does indeed have mod+prof autocalculation.

But your modifier is just 'how many evens up are you from 10 for your casting stat'

"Hmm lets see how people like this spell and what their experience is, using it ingame…"

Whole comment section of the Spell: "Me no understand, how Melle Spellcast working?"

But if you were to say, pin an iron weapon into a target, like a lance or spear and used shocking grasp you could have the effect your looking for. 

so if i use absorb elements from a mage that hits me with a firebolt then use familier to deleiver a shocking grasp could i use the melee attack dmg from absorb elements with the shocking grasp too?

Way I see it, you could build a hit-and-run Wizard around this...

Granted, Wizards have no business being in the thick of melee...but cast "Expeditious Retreat" on one turn for bonus movement...

On subsequent turns, bonus-action Dash and deliver a "Shocking Grasp".

If it hits, proceed to retreat out of there with your bonus movement.

If you miss..."Misty Step" to teleport to safety without provoking attacks of opportunity.

None of this breaks the concentration on "Expeditious Retreat"; thus, you are providing unique melee capability, while expending minimal spell slots...which you get (mostly) back on a short rest.

What is the Verbal Component to  Shocking Grasp?

Quote from LordMaou >>

What is the Verbal Component to  Shocking Grasp?

 That’s not something any spell specifies. Mechanically speaking, it just means that you have to be able to speak to cast the spell, and that others can tell you’re casting a spell.

Can you shock objects instead of creatures (such as water, to electrocute others outside of range)?