Should I approach them w/ $ to see if I can have the owner to close shop for 2~3hrs for the shoot?
How much money you got?
That would be a hardship for the shop owner, and pretty unlikely.
You'd be better off asking to shoot after-hours, or on a day that the store is usually closed on.
One of the films I'm currently working on shot in a store that remained open, with customers coming & going. It was a food store in a small town, though, so there were some very predictable busy & slow times that we could work with. (It also meant having to stop shooting at inopportune times, for someone randomly needing a quick sammich)
location release is the only form I need, right?
The shop proprietor might (quite reasonably) verify that your production has insurance to cover them, just in case of catastrophe.
You might also need signs to post in the area (especially if customers coming & going) that the area is being filmed, and that by being in the area they are giving their consent.
Do I need the location owner to sign the location release when...
1. I'm approach them prior to the shoot?
or
2. On the day of the shoot?
You'll want it signed any time before you start shooting. Sure, you can do it on the day of, too.
If you ask one store and they say no, there's always more to ask. Or friends of a friend, etc.
Good luck.