You can run a 4 or 5 cell receiver pack for the servo(s) and receiver, but it just adds to the weight and it's just one more thing to charge. Far better is to use a
UBEC to bring the main battery pack voltage down to 5 or 6 volts. This lets you use just one set of batteries - your main ones. The power needed to power the receiver and servo(s) is minimal compared to the brushless motor requirements so any difference in runtime will be neglible.
You CANNOT simply use a Y adaptor to directly power the receiver as the voltage would be too high. Even 2s would be too much. You do need a receiver battery pack or a UBEC (but as I said, the UBEC is a better choice IMO).
The ESC has a BEC built-in, but if you are running anything over 3s, you should definitely use an external one. The built-in one is a linear regulator and will heat up.