how to build rc transmitter and receiver with an old rc transmitter
If you are controlling an RC plane, you should probably just buy a transmitter and receiver specifically designed for that. They are cheap and reliable and will generate PWM signals on their own.

If you must use an Arduino for some reason, NRF24L01 are not going to cut it as they are not powerful enough to reach 1 km. You should probably look into something like an XBee Series 1. With about 60 mW transmit power, its range is up to 1.6 km.