How to subscribe to communities and threads on Lemmy with Mastodon?

I am trying to figure out how people can subscribe to a Lemmy community or Lemmy thread?

It might be possible to see a community on Mastodon if you copy the link (example: https://lemmy.ml/c/lemmy_support) and paste it into the search field on Mastodon and then you can hit subscribe and even activate the bell for notification.

But nothing happens if I do that.

Can someone confirm that it usually works like that, but it may be a problem of my Mastodon instance?

Is it possible to subscribe to threads, too, e.g. like this one here I wrote (without being the creator of a thread)?

I would really like to go public with my Lemmy instance, but if this doesn't work, it's a no-go.