1) The Futaba receiver can be run on 4.8 to 6.0 Volts, so that translates into a 4 or a 5-cell NiCd/NimH battery. Some ESCs can be set to supply 6V to the receiver (and servos) but most of them just supply 4.8V.
2) There are LOTS of mini RX's available. If you buy one, be sure it is a negative shift receiver (which matches Futaba's frequency shifting scheme) or get one of the newer ones that can "autodetect" the shift of your TX. Castle BERG receivers are pretty good. For park flyers a single-conversion RX is adequate, but you'll probably want to get a dual-conversion RX for any gas-powered or sailplane flying - they generally have a longer range.
3) The receiver "doesn't care" what kind of TX is sending a signal, as long as it's on the right frequency and properly shifted. The transmitter "doesn't care" what receiver (if any) is getting the signal, as long as the antenna is on the transmitter.