Sounds like you're trying to deal with 2 issues simultaneously and may be confusing the two.
A rim bumping into the pad for part of the circumference but having good clearance for the rest can probably do with some trueing.
Truer IS better, but for a casual-use hybrid 2 mm wobble or so is neither functionally restrictive nor critical.
Brake pads not returning is another issue, usually caused by cables dragging in their sheaths.
What's easier than replacing cables though is to increase the preload of the return springs. If you pull the brake arms off their bosses you'll most likely see 3 holes where the return spring can be anchored. Reassemble with the springs one hole up and see what happens. There's usually a small adjustment screw somewhere that'll allow you to balance the return between the arms as well.
If return springs are external you can bend them manually w/o any dissassembly.
If this doesn't do the trick there are only two places left that can cause drag, levers(unlikely), cables (likely). Fastest is simply to replace cables and sheaths, taking care that routing is smooth and as short and straight as possible.
When you did what?
Nah, trueing a wheel on the bike is a little more awkward than trueing on a stand, but there's no principal difference. Many a good wheel has been trued(even built) with the bike as only assistance.
You're tinkering and learning, nothing wrong with that.
