To elaborate on the water pump - if you are hooked up to outside water source, you do not need the pump turned on. It is only used if you are using from the fresh water tank, and in that case you can leave the switch turned on while you are camping, as it will only operate when the faucet is turned on. When you are finished camping, turn it off.
As for the tires, at that age they would be getting borderline condition in my opinion, even if you cannot see obvious age cracks or dry rot. Especially if they have been on the bare ground for an extended period of time. I just replaced mine this year ('06 and '07 manufacture) as I have seen what happens to your trailer when you have a blowout, not only that but I certainly think the risk of having a blowout on the highway is not worth taking the chance. Peace of mind and safety of my family is worth more than a few hundred dollars to me.