I want to ask about the jet fuel purchasing cycle. Is it the airport that buys the jet fuel from refineries and then sells it to the airlines? Or do airlines buy fuel directly from refineries?
The airport is buying fuel and selling to airlines. And more over, they provide different types of fuel on prior request by the airliner. Reference : VCBI
Airlines make direct contracts with the major petrol companies eg Chevron, BP, etc. for large quantities of JET-A, often years in advance of its use. It is the best way for them to buy fuel in bulk like that and it is traded much like stocks are. Airports themselves will fuel airliners with on-hand supplies of JET-A and be reimbursed for it by the petrol companies.
It depends. Airlines have contracts either directly with say Shell or they have a contract with a 3rd party that handles their fueling requirements.
That 3rd party may or may not be the airport, it could be another company servicing the airport (and maybe others as well).
And such contracts may well differ depending on location. E.g. at their home base(s) they may draw directly from Shell, but at remote locations where Shell does not supply fuel to they may buy fuel from Joe's oil and lube supplies.