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point number 2 do reply to the questions asked in point no. 2
Yes, message can be retrieve by transmitting only the side bands. In this form of AM (Amplitude Modulation) transmission carrier is generally removed or supressed , producing a double sideband with suppresssed carrier (DSB-SC).
Transmission is also possible with one sideband being transmitted.
It is possible to retrieve the message signal using both side bands but not using only one side band as the side bands formed are fc+fm and fc-fm. Using both these signals we can get back our message signal by first getting a signal of frequency 2fm by destructive interference and then downsampling it to frequency fm. Whereas, in case of only one side band we get only one frequency i.e., either fc+fm or fc-fm. So, it is not possible to identify the message signal as interference is not possible and we do not know the carrier frequency also.