Not any frequency, the radios have physical limitations that only allow them to transmit on a small range of frequencies. They can certainly cause interference outside of the bands they were designed to operate on, though.
Yes, any frequency. Remember we are talking about a faulty piece of electronic. With some pretty weird fault. Not just a transmitter operating in an almost normal mode.
Take an ILS (instrumental approach) frequency 108Mhz. Any piece of wire of around two feet (half dipole) can be a pretty effective antenna at that frequency. Say, headset cable + an output cascade of the amplifier self-excited at this frequency? Doesn't happen in real life, but still...
Are airplanes really that effective as faraday cages? If they were, it wouldn't be possible to use a cellphone inside one at all, and this wouldn't have been a debate to begin with.