Usually on this forum when an account is permanently banned all the posts and activities of the user gets deleted;
Not true. This only happens when the user gets nuked (mainly when the user is a Newbie with a recently created account).
(I) Will the merits given by the banned user remain?
(II) If yes, will it show the banned account username?
Yes. Nothing will change. The user won't be able to post or merit anyone, but the account will stay the same as before.
If I find the post I'll update here.
https://bitcointalk.org/index.php?topic=4560722