To answer the second question first then yes - you have access to all plugins including updates after your membership has expired. See the FAQ for this and other questions you may have: https://simple-press.com/membership-faq/

We do not currently have a chat plugin and this is mainly because there are several, I believe, available for WordPress. I honestly can't remember the names of the ones we have come across that some users have active - maybe someone else will be able to and will post here. Bit I am not aware myself of any outstanding issues with any chat plugins. The only two things I would say are that you do have to remember chat by it's nature is resource intensive and you will need a good server and an understanding host! And as far as Simple:Press goes - it may be necessary to turn it off briefly during release updates but that just means a couple of minutes every few months!