I have a question about putting on QR front wheel on a mountain bike.

Do I put the drop out slot onto the axle, as low as it can rest on the axle? Does that necessary make it even on both sides?

The shop said to try to center it the tire within the fork, and make sure the brake does not rub.

Yes.

Unless there is some damage to the fork, or poorly built wheel - it should.

... which should coincide with both dropouts resting on the axle, all bits being healthy.

Well, brake adjustment can be fairly independent of fork/wheel alignment, so first place wheel right between the fork legs, then look at brake adjustment. Don't move wheel away from fork alignment to fix an issue with brake alignment.

jho, I had a suspension fork where the wheel wouldn't align properly within the fork legs. Taking measurments on the outside of the fork didn't show any problems so it was an internal issue. I just used a round file on the dropout that the tire 'leaned' towards and several test fits to get the wheel centered. A quick release isn't designed to keep a wheel aligned when the axle isn't sitting on both dropouts.

Brad

OK thanks!

my next question is that does it matter how much you spin/tighten the adjustment nut is on one side vs the lever side.
because I had to loosen both side side by a few turns when taking the wheel out before,
Or is just loosening the adjustment nut would release the wheel eventually?

But I know the skewer slides inside the hallow axle so as long as I don't run out of threads on either end it is OK?
I know it's not that difficult just want to make sure

You might as well put the wheel to the top of the slots, because after some miles of pounding it'll be headed that way anyway. The best way to consistently mount wheels is to do so on the floor with the bike vertical. Let gravity settle the fork onto the wheel and close the QR. That takes any guesswork out of it.

If the fork is straight and square the wheel will be perfectly centered. If not, then either the wheel or the fork aren't correct. Try reversing the wheel to determine which, and if you're up to it, file the top of the slot as Bradtx suggested until the wheel fits perfectly. Work carefully because every millimeter filed will move the rim about six. Lastly the brakes are adjusted to the wheel and not the other way around.

There are different kinds of quick release skewers. On some, you can only loosen the nut side since the lever side is fixed to the skewer. But there are some where the lever side also screws onto the skewer. If this is the type you have, be careful not to remove that side. If it keeps coming off on you, you could put some loctite on it and screw it in the appropriate amount for future use and then most likely only the nut side would move when you spin it and you wouldn't have to worry about the lever side coming unscrewed.

It used to be that you adjusted the tension by way of the left nut just once, then the lever throw was enough to tighten or remove wheels. But those days are long gone and the lips on forks require that you loosen and readjust the nut every time with each wheel change.

QRs vary, but generally the nut should be adjusted so the parts make contact and begin to resist at about halfway through the throw. Start there, and fine tune trial and error, so it needs reasonable force to close the lever fully. Note that top dead center on the cam is 10-15 degrees before the full closed position, so it'll actually get easier in the end. That's what keeps it closed - the lever has to get a bit tighter before it can open.