If I backup and reset my android phone, will it keep my old number?

Yes of course. The phone number isn't tied to your phone permanently. You can reset your phones until the end of time and the phone number won't be removed.

You'll loose your number if you don't pay the bill, though.

Yes you will keep your phone number. The only way you can lose your phone number is for non payment for more than a month, depends on the plan you have.

you can keep you number as long as you have no overdue bills. But for the contact list, I am not quite sure.

It will NOT go you will keep it