What determines how narrow a radio channel can be?
Your actual questions don't seem to have anything to do with your first paragraph.

There is a theortical limit as to how much information can be carried in a channel of some bandwidth and signal to noise ratio.  Look up Nyquist-Shannon for deails.  After you decide what information rate you need to transmit and the minimum signal to noise ratio you expect at the receiver, the theory tells you the minimum required bandwidth to carry that information.

However, most common modulation schemes don't make use of anywhere near the theoritical maximum data rate for the given bandwidth and signal to noise ratio.  Early modulation schemes, like AM, were used because they were conceptually simple and obvious, and relatively simple circuits could do the modulation and demodulation.  The minimum bandwidth required for AM is twice the highest frequency you want to transmit.  This is because there are two side lobes, one on each side of the carrier, that must have the full bandwidth of the signals you want to send.  On the receiver side, there is no way to make a perfectly sharp filter, so carrier frequencies need to be spaced with some room between the ends of adjacent channels.  This gives the filters in the receiver room to not attenuate the highest frequencies of interest too much, but strongly attenuate the highest frequencies from adjacent bands.

The apparent extra information of HDTV transmitted over the same channels as NTSC TV came primarily from two sources.  First, digital encodings and being able to rely on significant digital computing power in receivers allowed for modulation and encoding schemes that used the existing bandwidth to carry more information than before.

Second, there is a great deal of compression applied to HDTV pictures.  This compression is carefully chosen to not send the parts of the signal that the human visual system is least likely to notice missing.  This takes into account that images are being sent sequentially too.  If you pause a HDTV stream, you will notice that whatever single picture it paused on looks worse than the continuous video.  Actually all the frames of the continuous video look just as bad, but the way information is deleted from them makes use of persistance of vision and the fact that your visual system will sortof average a few frames over time.  There is also significant compression in the two spacial dimensions.  Taking all three dimensions into account when applying compression (X, Y, and time), allows for some impressive compression ratios with little apparent loss in quality.