Should you get tasks from the backlog when everything is done in actual Sprint? Or it is a good time to keep learning while waiting for next Sprint?

If you have a backlog, your should be working on it. That's just my pinion, though.

Depends. If you have dedicated times for knowledge expansion, then yes, do the next things from the backlog. Better be ahead than behind

If you have a cunt company, use your spare time for good.

The only right way is to ask the PO!
Only he can tell if the backlog is already correctly sorted by priority and if the topmost ticked is complete and wanted.
Assuming things is the death of good communication which is vital to the agile way!