Technically you have time to make a brief city centre visit as it's only 12 minutes by train from the airport, but I doubt it's hardly worth it with only three hours between flights, you'll get about an hour in the city centre perhaps (of course that also depends on how well you know Copenhagen).
If staying at the airport there are plenty of shops and restaurants in the transit hall if you fancy some shopping.
Otherwise the lounge really isn't too bad, it's definitely one of the better lounges if you have three hours you need to kill.
There are TVs, plenty of newspapers and magazines, internet computers etc.
Regarding the seats you will keep them even if you don't check in online.