Yeah for the rear you need to center it by eyeballing the wheel so it is properly centered between the brakes and the stays. You cannot push it back all the way because the rear derailleur is there on a hanger.

For the front, I wouldn't sweat the difference between 95 mm spacing on the wheel and 100 mm fork; that's no big deal for a steel fork.

You should be able to clamp down the quick release hard enough so it doesn't move in the front fork. It may be that the front quick release skewer isn't doing its job properly which is why your wheel is moving on you. Replace the skewer and see if that fixes the problem. Also make sure the brakes are properly centered.

Then I'd check to see if the wheel is properly dished. Try a different front wheel to see if that solves the problem. If it does, the wheel is out of dish.

You have one of these right?