Sometimes QR will send you an e-mail offer for an upgrade (in my experience, it's usually only for some sectors - for me it represented terrible value). This is more of a rare occurence though.
You might be able to call up the call centre to upgrade if booked directly, otherwise you'd have to ask your travel agent. You'd probably be subject to a change/upgrade/admin fee if your fare permits it, plus the difference.
There is no bidding system from what I understand - I think I've only ever seen it on CX.
Airport upgrades from what I understand are only available if there are enough meals in J. No meals, no J - probably why the seats were empty?
No harm in trying at check in - unless you are asking for a free upgrade!