Does the building's caretaker deserve a commission for renting out an apartment, given that his role was limited to providing the owner's phone number, and no prior agreement was made with him regarding a fee?

The building guard who showed you the apartment and gave you the owner's phone number has no right to demand a fee from you for that, unless custom dictates his entitlement to a fee for such guidance. If custom dictates his entitlement to it, then you are obliged to pay him, even if he did not explicitly stipulate it to you; for "what is known by custom is like what is stipulated by condition."