I was wondering if I could shoot through a large creature like the image below?
On the right image, one of the players insists that a large creature shouldn't be able to fill up the 10x10ft space, therefore should still be able to shoot through the large creature (orange) and hit the red for maybe 3/4 cover (+5 AC).
What do you guys think?
Another question would be, can green magic missile red on the right image?
The only real guidance the rules (PHB) give us on this is:
A target with half cover has a +2 bonus to AC and Dexterity saving throws. A target has half cover if an obstacle blocks at least half of its body. The obstacle might be a low wall, a large piece of furniture, a narrow tree trunk, or a creature, whether that creature is an enemy or a friend.
(emphasis mine) From that, it seems like creatures provide half cover, no matter what.
Now, the DMG (p251) also mentions cover:
To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the square the attacker occupies or the point of origin of an area of effect. Then trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover. If three or four of those lines are blocked but the attack can still physically reach the target (such as when the target is behind an arrow slit), the target has three-quarters cover.
(emphasis mine) which also only calls out half cover for creatures.
All that said:
You and/or your DM may interpret the rules differently, as the rules don't explicitly say "creatures can (or cannot) provide 3/4 or full cover" and some cases are going to be outside of the generalization of my answer; i.e.- a gargantuan creature laying on the ground would likely provide a solid obstacle to creatures on either side.
Though, if an attacking creature can see at least as well as looking through an arrow slit, no more than 3/4 cover should be offered, as an arrow slit is specifically called out.
First of all, let's just clarify what you mean by 'shoot through'. I'm assuming you're asking if you can shoot through the space occupied by the creature, not physically through the creature itself.
To understand the difference, let's look at how size interacts with combat. According to Player's Handbook, Ch 9: Creature Size:
Each creature takes up a different amount of space. The Size Categories table shows how much space a creature of a particular size controls in combat.
According to the provided table, a Medium (you-sized) creature controls a 5' by 5' space during combat. Does that mean that you physically take up an entire 5' square? Of course not.
The same applies to size Large creatures. The table says a size Large creature controls a 10' by 10' square. Take a size Large creature like a Dire Wolf. They're the size of a small horse, yet they still don't physically fill the entirety of the area they control during combat. Sure, it would be harder to hit someone behind them, but that's why there are rules for cover.
So, yes, in both of your diagrams, Green would be able to attack Red, even though Orange is in the way*. Whether you hit or not, well, that's up to the dice!!
Now, for your second question: Even if you can only see the BBEG's finger, you can still Magic Missile them.
Each dart hits a creature of your choice that you can see within range.
No to-hit roll, no credit for cover, as long as you can see them, it's PEW-PEW time.
*The caveat is that there are some creatures, such as the Gelatinous Cube, which actually do take up their entire space...but all of these creatures specifically state that they do so in their description. If Orange was one of these rare cases, then Red would have 100% cover and could not be hit.
