If I am using a channel only for morse code (CW), with one frequency and interruptions for dots and dashes, is the necessary bandwidth of the channel twice the audio frequency of the tone used for CW?
If I pushed my doorbell button I'd hear a tone coming from the thing that makes the sound but that sound is not coming from the doorbell switch - it's on-off dc coming from the doorbell switch (because it takes two batteries to power it). The tone is created inside the wall thing - it recognizes the doorbell switch and activates an oscillator that sounds.
Similarly CW morse code works with a carrier that is turned on and off by the switch - the carrier is not the tone you hear but the carrier is (or can be) used to gate a tone generator at the receiver - the carrier can also be used to create the tone more directly by mixing it (at the receiver) with a frequency of similar frequency - this creates a difference frequency that can be audible (even though both received carrier and local oscillator are not).
The bandwidth of the channel therefore only needs to be a few hertz - enough to be able to recognize a dot from a dash at high transmission speed. However, if your morse code modulator is a bit crap it may generate a much wider bandwidth that can interfere with other stuff tuned close by.
Yes. The rules of aliasing still apply. "Interruptions", by the way, impact the frequency content of the tone. The resulting spectrum is the frequency of the tone CONVOLVED in frequency space with the windowing pulses (windowing multiplication in time maps to convolution in frequency), so your frequency content is fairly higher than that of your tone.
As Chris points out, the bandwidth, as opposed to the spectrum, is a function of the pulses (though that bandwidth will be displaced by the tone frequency, the carrier frequency).
The transform of a pulse, though, is going to have frequency content that is mainly at the frequency of the pulse, but there is energy at high frequency at the fast transitions (see http://faculty.kfupm.edu.sa/EE/muqaibel/Courses/EE207%20Signals%20and%20Systems/notes/FourierS/Figure%203_11%20Spectra%20for%20periodic%20pulse%20train.jpg) -- it takes the form of sin(pi*x)/(pi*x), and has "side lobes" that can go on for quite some time in frequency.