Other than the small, dedicated comedy venue on O class ships, you are very likely to be able to get into any show on any ship, regardless if reservations are available or not.
That same app will list all of the other things happening on the ship. You can set it to the sailing (not yours) to see the current info and assume things will be very similar on your sailing.
Welcome to CC.
Most rotations are 10-12 weeks so you can estimate given the current schedule. You can look in some Ovation related threads to see if Captain info is passed on.