qcop [they/them]

Basically your post is already “posted” there. Anyone with a mastodon account on an instance that federates can see it. They could either paste on their mastodon search interface the url to this post and see it appear as a mastodon message. They could then reply on mastodon and it would show for you here on your lemmy instance.

They could also follow your account on mastodon or a community just as if you were a mastodon user and then see your posts on their timeline.

I have no idea for your first question.

Yes I’m sure but it depends on your theme. For example, Shydactyl theme must be customized to display favicons

Tridactyl? I prefer it to vimium due to native messaging support