If your thermostat looks like figure b4 on page 18 of the document referenced above (4 button model), they are prone to dirty connections inside the unit. If that is not your thermostat, then the rest of this post is worthless to you.
I have the same 4 button thermostat like figure b4. I've had fairly good success removing the thermostat from the wall and spraying with contact cleaner and then working the buttons several times. Eventually, the small metal contacts inside the buttons will bend and not make good contact. You can disassemble the button assembly and attempt to bend the contact back into position, or you can reverse the contacts since only 1/2 of it is used when you push the button. CAUTION: DISASSEMBLE CAREFULLY. If that little spring goes flying about your coach, you'll spend a lot of time on on the floor looking for it. (BTDT). :)
Try the contact cleaner approach first. I generally have to clean mine once per year. I use spray contact cleaner purchased from Radio Shack.
Last year, there was a vendor on ebay that rebuilt these thermostats, so that is a possibility. I don't know if the vendor is still on ebay, but worth a look if your thermostat is defective. The 4 button model is obsolete, so the manufacturer's solution is to upgrade to a 5 button model but that option is much more expensive than fixing the old 4 button model.
Regarding your questions
1. How do I get it to change zones? Seems to be hit or miss!
2. Can I shut off one zone completely? And if so how?
Depressing the top 2 buttons will let you select the zone. You can run one or both zones in the heat pump or a/c mode. It will become intuitive once your thermostat is working correctly.
Fred