Aside: Having "worked" in online communities in the past as a volunteer moderator, please take my answer with the pinch of salt it likely deserves.
1 - When the user attempts to login
Tell the user that they've been blocked from contributing to the community and give them the reason why (all this is subject to the platform you're using supporting this, of course!). Also, give them an avenue to respond / make contact. If it's a temporary ban and you want the user to re-join the community once they've cooled off, providing a way to "vent"/"feel that their voice has been heard" may well help.
2 - When the user attempts to reset their password
None of us are perfect. We all (or some of us!) know that we shouldn't use the same password across multiple sites. But we all (for a given definition of all!) do. Sites like Have I been pwned? allow people to find out when their credentials have been compromised and there should be no impediment to them then changing their password on any and all sites/services they use so that their accounts/online personas remain secure. There's nothing to gain in preventing a blocked user from changing their password (or email address), and everything to lose for the end user concerned.