Yes of course, unless they notified you that the open box item did not include a remote.
Yes, most definitely. Just remember that an extended warranty is MORE important BOTH SEPARATELY on electronics & goods who's packaging are disturbed; therefore in your case you have not 1 excellent reason, but 2
Yes, you always get a remote
Yes, unless otherwise mentioned prior to purchase.
Yes - do just as Joe advised
Yes, just be sure to ask a service rep before you leave the store or you might have to make another trip.
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