1. Should not be an issue; checking bags all the way through is common on all itineraries with layovers <24 hours.
2. The mall close to the airport is open until at least midnight. My daughter and I took a taxi there around 22.30, and there were still kids with nannies in the play area when we arrived. They seem to close around midnight. The flight to JFK was around 4am IIRC.
3. I have a 12-hour layover later this week (JFK - AUH - CGK), but in the cheapest Y category. I booked a hotel room near AUH for <100 USD, but to each his own.