At the moment, yes, most of it is being hosted by hobbyists, some places are accepting donations. I don’t think there’s been much in the way of creating non profit organisations or other official structures to ensure continuity (although I admit not looking to heavily into it).

It is entirely possible for instances to blip out of existence if the owner decides to close up shop. But that was also the case for Reddit and other social media platforms, however those are in it to make money, which is a strong motivator to keep going.

Increased server load from reposting could have an effect on servers if it causes an extremely large increase in data. At the same time it may cause efforts to streamline and improve efficiency to be bumped up the priority list. However it would have to go on for quite some time I think to cause large issues?

Sorry there’s so many "maybe"and other ambiguous terms in the comment, it’s really not a simple yes or no.