Can you tell me which community site you are referring to? Are you a member of a community or an owner/admin?
Crowdstack can be configured any number of ways and it does support a "remember me" option which allows members to stay signed in beyond their current session. Of course, every site will configure it differently.
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .