No. I think what confuses people is that you usually don't go to any particular instance but rather you access that instance through your home instance. e.g. you search in kbin.social for a lemmy.ml community or post. They'll show up.
You can still directly to that other instance. But you can't comment or vote. You would need to copy the full fediverse url for that post and pop in the home instance's search in order to take actions on the post.
afaik there isn't one. Maybe it's incoming? sh.itjust.works has both save and collapse functionality. So it is possible. There are also starting to be some apps floating around out. Jerboan (Jerboa?) is one of them. They might have the ability to save stuff.