Yes, you can shoot through a large creature's space to hit the smaller one behind it.*
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
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.