Relevance of Input and Ouput size of PRF on CTR mode
My solution

I think I've found a solution, there was a lack of comments/answers so I will post it as an answer in order to conclude this. 

I'll begin with part (b). 

Cycles in the counter must be avoided, that is, it must be ensured that ${\tt ctr}, {\tt ctr}+1,{\tt ctr}+2,\ldots$ never reaches ${\tt ctr}$ again. Notice that ${\tt ctr}\in \{0,1\}^{\ell_{\text{in}}(n)}$, so it must be ensured that the maximum block length $\ell(n)$ does not exceed $2^{\ell_{\text{in}}(n)}$. That's a constraint between ${\ell(n)}$ and ${\ell_{\text{in}}(n)}$. $\ ^{1}$

On the other hand, in the proof of the CPA-security of CTR mode the "birthday" term $2q(n)^2/2^n$ appears bounding the probability of a successful attack compared to guessing, where $q(n)$ is the maximum number of blocks (so $q(n) = {\ell(n)}/{\ell_{\text{out}}(n)}$).
This term must be negligible, and that is the restriction between ${\ell(n)}$ and ${\ell_{\text{out}}(n)}$.

Regarding part (a), I claim that there is not any constraint between $\ell_{\text{in}}$ and $\ell_{\text{out}}$ as long as $\ell(n)$ satisfies the conditions mentioned above. This can be seen by revisiting the proof and checking that it holds independently of the polynomials $\ell_{\text{in}}$ and $\ell_{\text{out}}$ (so yes, the ratio $\ell_{\text{in}}/\ell_{\text{out}}$ can be anything).



$^{1}$This is assumed in the proof of CPA-security on Katz' book when they say: the values $f({\tt ctr}^∗ + 1),\ldots,f({\tt ctr}^* + \ell^*)$ used when encrypting the challenge ciphertext are uniformly distributed and independent of the rest of the experiment