RE: Parkzone f4U Corsair Rtf
Not too sure if the DX5 can be fitted with a normal Tx type rechargeable battery... but, you can put AA type recargeable batteries in it. And from what I've seen, even in Tx's that use AA type batteries there is always a battery level indicator so you should be able to tell if you need recharge or get new batteries.
You are correct about the AR500. It uses the newer DSM2 modulation, the older DX6 Tx uses DSM1. If I'm not mistaken you can use a DSM1 Rx with a DSM2 Tx but not the other way around.