Will I be able to follow various users across the Fediverse and view all their posts in the Threads app, or will I just be able to sign in to their servers with my threads account?
Yes, using the Threads app you could then follow somebody from i.e. a Mastodon instance if that instance does not have the Threads domain blocked and the particular instance user also does not have it blocked. So it's going to be hit and miss.
And no, I don't think you can log into another server using your Threads account.
If it's going to function like any other Fediverse app, which I assume for now, then yes. You can follow people across instances and have both a local and global feed.