When you click on a community you can click the "block community" button at the top right-ish part of the screen, it's in the same section as "create post" and "subscribe"

Searching is a little more complicated, to keep it simple you can use the built in search. That will show you communities in the instance you're searching on, and any community that anyone else on your instance has accessed.

To search all(not all but majority of) communities across all instances you can use this: https://lemmyverse.net/communities

Each instance is like its own little island. Some islands have a theme, some are general purpose. And the instance you make your account on is where you have your citizenship, but you can view and interact(follow,comment, like, etc) with other islands that allow visitors from your island. If an island(instance) doesn't want to allow visitors another island, or allow their citizens(users) to go another island the mayor of the island(admin) can cut off contact with that particular island(de-federate)

If the feed seems to be stagnant, you could be using the (default in many cases) active sort, which tends to have a lot of the same posts at the top, from what I've seen. Switching the sort to hot generally shows more fresh content in my experience. You can block communities on the web version using the red button on the right, in what I think is the sidebar, although that might be hidden on a phone. This site looks to be helpful for finding communities as well.

If you mean your read posts stay there forever, go to settings > hide read posts. So much better.