Is it possible to make a cell phone transmit arbitrary radio waves at a certain frequency? Or does the Mobile OS only allow higher level access?
If the answer is 'no' as I expect it is, is there any way to make a phone talk to another electronic device remotely without handshakes and the like?
There are pretty strict regulations on what frequencies mobile devices can use. The firmware will therefor block almost all possible accesses. (Let alone the fact that it won't be exposed in an API)
But there are plenty of more suitable solutions for short-rage contact - IR and bluetooth.
Probably not - as EFraim indicated, there'll be regulatory frameworks in place to say that devices of type A must use frequencies in the range X-Z with no more than a certain power output.
Additionally there's physical issues as well as to be able to broadcast at different frequencies requires different length antennas, certainly if you wanted to broadcast in the UHF range, the length of antenna would be radically different to the microwave-range that mobiles use (2.4GHz). Failing to match the antenna to the frequency can produce all sorts of odd effects that can destroy the output circuit.
Thus the only items available are going to be those that the phone itself presents - namely bluetooth and infra-red (if it exists). Some phones also have WiFi as well, so it really depends what you actually need this for.
The question is general, so the answer is going to be vague as well.
You can't do that in mobile phones, the hardware is usually designed for a certain frequency band, which means that the Antenna, Power Amplifier and the Oscillators may not be able to transmit outside that range.
A practical answer, without involving any knowledge of physics:
If you could do that, adding a new band to a mobile device would be simply a matter of updating the OS/firmware... and it seems a little bit more complicated than that.