Does exist in this forum ban list (list of banned users)? Does "banned" label under the user avatar mean permanent ban?
You can't see how long a user is banned for. There is a modification in vBulletin to show a custom banned list page with all banned users and their duration of ban, but it's not installed here.
Well the only way to check if the user is banned by checking his/her post in the threads. Or just search in the top right hand corner and put the username, it you cannot view the profile page, which means the user is banned. Banned does not mean permanently banned, it might be from 7 days to 3 months
7 day bans no longer exist. The duration of the ban is determined by the number of infraction points a user has. When they have fewer than 10 the ban is lifted. That might be hours - or it might be 6 months. and even then we have to wade through the infractions to see when the count will drop below 10. Only the user gets given the actual date and time. Seeing all the banned users would just encourage spammers to sign up and use their domain as their username so that curious viewers could go to their site. It would be far more useful to have the return date shown on their profile, however the uncertainty possibly creates a further disincentive.