How many "compressible" strings are there?
A simple counting argument shows that the number of strings of length $N$ such that $K(S) \leq M$ is at most $2^{M+1}$.

Conversely, considering the program $\Pi$ that gets an integer $r$ and a string $x$, and outputs $x$ together with $r$ many zeroes. Going over all strings of length $\ell$, this gives us $2^\ell$ many strings whose complexity is at most $\ell + O(\log N)$. Choosing $\ell = M - O(\log N)$, this shows that the number of strings of length $N$ such that $K(S) \leq M$ is at least $2^M/N^{O(1)}$.

This answers your first two questions up to a small multiplicative error. I suspect that the answer to the third one depends heavily on $N$.