1. Correct. Just because Mastodon doesn't use a term, doesn't mean the Fediverse as a whole doesn't use it yet. For example, the community page on Friendica is pretty much the same as the federated timeline on Mastodon. And you cannot force a 13-year-old project (Friendica is older than Diaspora*, not to mention Mastodon) to change its lingo so you can re-define a word previously used by it.

2. The danger here is that most people only know the term "server" from Discord where a "server" is a glorified chatroom which resides on the same actual server as all the other ones. That's their definition. If you talk to them about, for example, your own Akkoma server, you might mean a dedicated piece of hardware, maybe a machine running at your home. They, however, are likely to believe you refer to a chatroom or community which you've created on a centralised online service.