How are large cargo aircraft loaded at airports?
They will be loaded/unloaded on the ramp somewhere, 

In the case of a facility like the one UPS owns in Louisville KY. they will have a large amount of ramp space in and around the facility which is on the field. 


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The aircraft will pull to the facility as they would a gate and be loaded there


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In the case of just more generic cargo loading and unloading at an airport where no shipper has a facility the airport authority or FBO may have a facility set aside for cargo like the one at JFK. You can find a full list of the airlines/operators who have facilities at JFK here as an example. You can find a full map of the JFK cargo facilities here.

Keep in mind that some cargo will go on passenger planes and may be loaded at the gate. Along with everything else. In this case the cargo will be accepted and sorted (most likely at one of the above example buildings) and then towed over to the aircraft.  

Airport fees here in the states are often charged by weight so the fees to the field will be judged on that. The fees for the cargo operations will most likely depend on what you need done such as loading/unloading, storage, customs, refrigeration, live stock services etc. I dont see any explicit prices listed but here is another one of JFK's cargo handlers CAS, I would assume you could contact them if you wanted some pricing on a given transaction.  

I would not think the reinforcement is any different than anywhere else, a fully loaded aircraft be it cargo or people is the same weight.