Practical implications of the switching lemma and the counter mode security bound
Does this $q^2 2^{−l−1}$ just show that there is no attack that is better than this bound, or does it also give us an attack? And if so, what does that imply?



The switching lemma is tight up to constant factors. If you make $q$ queries, then you can indeed distinguish between a PRF and PRP with probability at least $0.632 q^2 2^{-l-1}$. Here the 0.632 is $1 - 1/e$. More specifically, this is the probability that you will see a repeated output by a PRF (and obviously a repeated output from a PRP is impossible).
You can indeed attack the IND-CPA security of PRP+CTR with this advantage. 

Suppose you ask for $q$ identical blocks to be encrypted. Assuming the IV+counter never repeats, it is not hard to see that there will be no repeated ciphertext blocks under a PRP.

Suppose you ask for $q$ uniformly distributed blocks to be encrypted. Then the ciphertext blocks will be uniformly distributed and therefore display duplicates with the above probability.



  Is $q$ the amount of queries that is allowed by the oracle and thus, assuming no other leaks, the total amount of cypher calls by my system?


In this context, $q$ is the number of calls to the PRP that the attacker induces the honest party to make.