A bank offer is an instant discount applied at the payment step when you pay with a qualifying card, usually capped at a fixed rupee amount. It is separate from any store coupon, which is why the two can often be used on the same order. The card and the cap are the two things to check before you count the saving.
It comes off at the payment screen when you select the qualifying card, rather than being refunded later. There is almost always a minimum order value and a maximum discount, so a "10% off" offer capped at ₹1,000 stops helping past ₹10,000.
Usually yes. Store coupons come off the cart total first, then the card discount applies to what is left, so the two are counted separately at checkout. The order matters for how much you actually save, and a few sale-event coupons are excluded from card offers. Check the final amount on the payment screen before you pay.
The page stays up and gets marked expired instead of being deleted. The buy button switches off and the listing shows what the price was, so you can tell an ended deal from a live one rather than landing on a broken link.