Do high frequency oscillations use more than one bandwidth Please excuse me for asking such a basic question. I was having a look at how AM radio works. So there is a carrier frequency and a higher frequency inside that that carries the data.

Does this mean that there would be two frequencies, one high and one low?

What about for stuff like 3G/GSM when stuff is sent over EM would it create noise at other frequencies, say out of their licensed spectrum?

If not how do they squeeze it all into such a tiny band of frequencies?
A modulated radio signal has non-zero bandwidth.  The modulation signal that carries the information has a much lower max frequency compared with the carrier frequency, keeping the total bandwidth (carrier plus both modulation sidebands) of an AM signal within FCC legal limits.

Other modulation schemes are used for GSM/3G, such as OFDM, that create more widely spaced sidebands, but the carrier frequency is so much higher (GHz range) than the modulation sideband width, that the resulting signal bandwidth is only a tiny fractional slice of the total RF spectrum.