One Little Question

I have no idea but have a bump. Maybe someone can help.

Maybe. There's no log AFAIK (apart from recent group joins), so it's tricky.

Future removals: You need a tool (e.g. a website or userscript) which keeps track of the groups you're in. It should be possible to make, but no idea if there already is one. I remember that ESGST can synchronise Steam user data, probably including groups. But not sure if it shows changes (e.g. when manually synchronising).

Past removals: I think a removal usually means that you can't join again unless invited. So you could check groups which you might have been part of, and if it's a public group but you can't join, then you have been removed from it. Not sure if there's any indicator in case of private groups. If it's a group where you can request to join, maybe such a request isn't possible any more.

i dont think so

esgst sync does show added/removed groups on manual sync