The letter 'c' in <cmath> refers to a group of C library functions.
By analogy, <stdio.h> may be included in C++ as< cstdio>, and as C lacks templates, nothing in <cmath> does either.
Aside from that, what benefit would parameterizing the type provide?
These functions accept and return doubles, which you can always convert to an int or a float if necessary.
On the second issue, I stand corrected: as M.A. and Francois Andrieux point out, there are occasions when this might be advantageous.
However, I believe the answer still applies in terms of <cmath>.