The lowest level I play is platoon level. For that level it’s usually Chain of Command, or sometimes Battlegroup.
As for basing, it’s a mess! I have 15mm in teams based for Poor Bloody Infantry (a company level game) for Russians and German Heer, but I also use them for Battlegroup and CoC which require individual figure removal. I just place a die behind the base to show how many men are left. But I ended up liking CoC so much, that when I painted up French and Fallschirmjager, I did so by basing them individually. And just to confuse the issue even more, my Commonwealth and German Heer in 6mm, are all based as teams, actually on the same size bases as my 15mm!
“Never” would be my answer for the final question, but I’d certainly have no objections to playing at squad level, if a set of rules appealed to me. Actually, come to think of it I used to play that type of skirmish. It was on the floor of my bedroom, using my collection of Britains 54mm figures, with books and toy blocks for terrain and – I think – Featherstone’s rules as I had just discovered his books in the library! But it’s been awhile….