On mobile browser to limit the feed to local, it looks like you want to tap the top left "hamburger" menu (three horizontal lines), then the triangle icon to the left of the cog/gear and set federation status to off.
For minimizing/collapsing comment trees, I don't think that's been implemented in kbin yet (a small reason I'm on Lemmy instead tbh).
As to subscribing or saving posts, I can't say without being on there. The closest I can see from my outside perspective is boosting a post, which seems to act like favoriting/bookmarking in other contexts. I don't get the sense that it's intended to be used as a subscription/saving method, but it may have to do for the time being. Other kbin folks may have better insight here than me though.