yes. no. maybe. up to you. Most people just use a similar binding from the store. I don't test new boots with bindings till I get home and have never had them not work together, maybe I'm just lucky. You could bring a binding along just in case.
Worse case scenario you can always return the boots for some others, but I find its easier to find a new binding that fits well instead of a new boot that fits well.
YES. However if they are the same brand and close to the same season you should be fine. The problems can arise when you buy boots much newer than your bindings or different brands.
I once made the mistake of buying boots that did not fit in my bindings. I had to beg the shop to let me return them. They did not do returns on boots. So if you buy boots with out fitting them in your bindings, make sure they accept returns.