carrier frequency limitations and bandwidth

Hello Forum,

Consider a baseband signal of a certain bandwidth B.
Using analog modulation (either AM, FM or phase modulation), in a single
channel environment(i.e. not worrying about possible interference between
multiple users and channels) can we impress that bandwidth B on carrier of
any frequency f? Does the carrier frequency need to be always much larger
than the bandwidth of the signal it carries (even in a single channel
situation)? Or is there some limitation?

Usually we are in a narrowband situation: B<<f. Would it be ok to have
B>>f?
If not, why not?

Let's think of a  pulse of light of duration T. If the period of the
carrier frequency, which 1/f, is larger than pulse period T, then the pulse
will not even contain a whole cycle of the sinusoid....is that a problem?

thanks
fisico32