1. That would depend on whether you use other cashback sites. Some may offer more (assuming you are going for cash and not rewards in the UR Mall) for hotel or flight bookings. If you value UR points more, then yes, it will make more sense to book with them. I haven't checked recently, but I thought the prices were the same as the official websites for the hotels/airlines? It should redirect you to the official website unless you are booking through an OTA (ex: Travelocity). But still, the price should be the same as if you went to the Travelocity website since it just redirects you there from the Chase website.
2. You should still get the membership benefits but you might not get the same points (or any points) depending on the hotel/airline policy especially if it's booked through a third party website like Travelocity.
3. It looks like members that have problems with their points posting for these purchases usually will get it resolved by sending a SM to Chase.