Today I realized that there seems to be a few feature of the StackExchange website, i.e., it seems that we can form teams to share and discuss topics in specific fields. To be honest, I do not know how does that work? For instance: (i) How can we see the existing teams (i.e., teams that have already been formed) and how to join an existing team? (ii) If I want to form a team for studying areas of my personal interest, how can I invite some other people to join ? My questions are definitely not exhaustive, and thanks for your help!
In the interests of saving people a tiny amount of effort looking on Stack Overflow, this post: Stack Overflow for Teams is now free for up to 50 users, forever seems to explain the changes and provide other links regarding them.
(i) How can we see the existing teams (i.e., teams that have already been formed) and how to join an existing team?
These Teams are essentially private SE Communities, with the same Q&A format especially as StackOverflow (a bit more dark mode and WYSIWYG than Math.SE). So I doubt there is any way to "see the existing teams".
(ii) If I want to form a team for studying areas of my personal interest, how can I invite some other people to join?
You can perhaps create your own team, as I did. It picked up my credentials from my StackOverflow account, so you may find a different experience. Once your team is created you will be able to invite team members based on submitting an email address for each one. (I think the invitations expire in a week.)
Up to now certain chat rooms have served in this fashion, for studying areas of common interest. The Teams environment is not "chatty" but meant to expose content useful for the group in a Q&A format. I'd guess that some groups who find their combined efforts productive in chat will benefit from migrating to Teams, but that most will not.
Just as a heads-up, it appears that MathJax is not enabled on any free team.
Perhaps it is an optional feature available only for upgraded (paid) teams, or one needs to request for it to be enabled on a per-team basis, but the latter seems overly optimistic to me, honestly.
In any case, I think the free Teams feature is less useful for members of this SE than for others.
As suggested in the comments, a workaround is to use @robjohn's bookmarklets for rendering MathJax. Just be sure that you've turned on the "Markdown" option in the new Stacks editor: somehow the dollar-delimiters do not work well with newlines otherwise.