Airman is right. Manufacturer doesn't matter. Frequency does. Both the transmitter and receiver have to be at the same frequency, and what's more, both have to have to be using the same band in that frequency range. My RC radio, for example, uses the AM 75 MHz frequency (which is what is normally used for ground based hobby radios). There are many other frequencies as well--the 27 MHz frequency is usually used for air based hobby radios, although I've seen some ground based in that range as well. Then, inside that frequency range, both the transmitter and receiver need to be on the same band, which is basically a sub-section of the overall frequency range. This band is determined by the crystal used in both the transmitter and receiver (the crystals will have numbers on them that represent the band). If both the transmitter and receiver use the same frequency and band, they should work. You can NOT put a crystal from frequency A in a radio that uses frequency B to turn it into a frequency B radio... they're the crystals only work with their specified frequencies.
As for your other question... I can't be 100% sure on this without looking it up again, but I believe the standard hobby RC signals use TDM (Time Division Multiplexing) to transmit their signals. That means a pre-determined amount of time is allocated to transmitting and receiving ch 0, ch1, ... ch n. So, for example, if you have an eight channel transmitter and only a 2 channel receiver, the receiver would be receiving the transmitter's channel 0, 2, 4, and 6 signals on it's own channel 0, and the transmitter's channel 1, 3, 5, and 7 signals on the receiver's channel 1.
So short answer, no, I don't think it would work. But I could be wrong.