When I un-check the subscribed folder and press OK then this folder is still subscribed = BUG!?

You can check the log to see if Opera is really issuing the unsubscribe commands and that the server is executing them.

Perhaps they get unsubscribed and the UI just doesn't update right away. If you unsubscribe, you might have to switch to offline more and band and check/send for the mail panel and UI to update. Or, you might have to restart Opera for the UI to be updated. If that's the case, then it's a UI bug. If not, the log might reveal what's up.

Add - create a new folder who is automatic subscribed.
Edit - on only few folders it change a folder name, on rest of them it's do nothing, next BUG!?

Might be the same issue as above.

Delete subscribed folder from IMAP server with e-mail in it.
Help button open the same F1 Help.

Hmm, that's weird. Sounds like a bug. Does the IMAP folder get deleted after a restart though? If not, as a workaround, try unsubscribing from a folder before you delete it.

Also, this stuff might happen with just the server you're using. Best to check with another mail provider.

Since Opera is no longer being developed, you'll need to use whatever workarounds you can like using the webmail or another IMAP client (like Thunderbird) to manage IMAP folders.