You need to make Palo reservations as soon as possible after boarding. In my experience, it isn't hard to get a reservation on a 7 night cruise--it might be difficult to get the date and time that you prefer. If you can't get what you want, you can always be placed on the wait list, which frequently comes thru. With the earlier boarding, they might not even be taking reservations till after you've had a chance to have lunch.
Unfortunately, a lot of people have learned the "game" to get more than one night at Palo's. If you are travelling with friends or have 2 cabins for your family, you can make a reservation for each cabin. For example, you are in 6000 and your friends are in 6002. You each make a reservation for 4 on different nights. Then each family enjoys 2 nights at Palo. It rather defeats the idea of one reservation per cabin. However, frequently people who eat there once will then cancel their "second" reservation.
As far as I know, there is only one menu in Palo's at dinner.