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Can I ask what card this is exactly? Anyway, to answer your questions: 1) it almost certainly should qualify since it's a purchase, and 2) they're obviously going to send you offers but you shouldn't feel obligated to take any of them. If you have a use for the gift cards you're getting then by all means go for it, as long as you believe it's a financially sound decision and you will pay off the purchase in full.
Yes!