Does this champ frequently get played in Pro Play?
Pretty much only Lee Sin out of this list is played in pro play. This is also pretty much the only place where I would consider him viable, he isn't really that good of a Jungler right now as there are other champions who are also strong early, but also have decent late game, and not being as team dependent.
What are these champions major counters
I'd argue none of these champions really have significant counters, this isn't DOTA 2 where a hero in that game can make you obsolete. The only one I can think is maybe Rek'Sai or Nocturne for Lee Sin as they can both negate his Q which is a major portion of his kit's power.
Who does this champion counter in the jungle?
None of these champions really counter anyone. In LoL you have early, mid, and late-game champions, which is actually starting to phase out, but basically early game beat non early game, so Lee Sin and Graves beats most people early on, and the other picks aren't the best early (more mid-game focused, like VI or Shyv).
What s the purpose of this champion?
Lee Sin wants to abuse his early game strength to end games quickly before he falls off. Graves wants to do the same but he can also power farm while doing so as he clears quickly. Vi wants to fight 2v2's and doesn't really want to 1v1 as much as Graves and Lee. Shyv wants to farm up and become a beast, but also take ganks when they are available
Lee Sin is a diver (Has ways to get on top of people, kind of like a tankier assassin with less damage but more CC). Graves is a range bruiser, he is short range but pretty good at dueling, has plenty of burst, usually wants to have his team engage for him. Shyvana is a diver that's weaker than Lee Sin early but stronger than him later in the game. Vi is also a diver, who has a guaranteed way of getting to her target.
How complicated in the champion?
Lee SIn is ridiculously difficult to play even at a mediocre level, you'd be trying really hard just to win half your games. Graves isn't the hardest but not the easiest either. Vi and Shyvana are very easy, good for beginners.
How likely is he/she likely to get banned?
Lee Sin gets banned alot, but not like Pyke or Blitz level bans. The rest don't get banned pretty much ever.
Is this champion squishy?
None of them really, maybe Graves... sort of... he gets armour from his E, so he's pretty tanky especially with life steal. The rest straight up build tank items so no.