Variable versus fixed costs in the airline industry I want to list the costs airlines have to sustain by distinguishing them between variable and fixed. Variable costs change in proportion to aircraft usage. Fixed costs show little or no change in proportion to changes in activity.
This is an incomplete list I took from the FAA website (here)
Variable costs:

Fuel and oil.
Maintenance (e.g., maintenance labor, parts airframe/engine/avionics, engine restoration, thrust reverser overhaul, propeller Overhaul).
In-ground and in-flight crew salaries (can also be thought as fixed costs).

Fixed costs:

Parking and hangar fees.
Insurance.
Aircraft modernisation.
Computerised maintenance management program.
Weather service.


Question:
(1) In which category should I put

Landing fees (ATC, runways, taxiways, parking at stand or apron for a certain time (e.g. 2 hours), use of gates / fingers / terminal for disembarking).

Lounges fees.

Scheduling coordination.

Surcharges or rebates in addition of landing fees (for noise, peak-hour operations)

Passenger charges

Administrative cost (managing/issuing tickets, etc.)

Overflight fees


(2) I'm fundamentally confused about the distinction between fixed and variable costs. For instance, landing fees increase with the number of flights and, hence, with the demand of tickets for a given route. Should they be classified as variable costs for this reason? Is this the same reason why fuel and oil, maintenance, and crew salaries are classified as variable costs?
I’ll address your second question first.

I'm fundamentally confused about the distinction between fixed and variable costs.

Simply put, variable costs are ones that go away if you cancel a flight (or, more likely, a pair of out-and-back flights) while fixed costs are ones you still have to pay.
A challenge is that many “fixed” costs are actually step-variable costs. For instance, if you cancel enough flights, you might be able to reduce how many aircraft or gates you need. But with the black and white dichotomy given, we classify those as fixed.

Landing fees (ATC, runways, taxiways, parking at stand or apron for a certain time (e.g. 2 hours), use of gates / fingers / terminal for disembarking).
Surcharges or rebates in addition of landing fees (for noise, peak-hour operations)
Passenger charges
Overflight fees

If you don’t land, there is no landing fee, so that’s variable. Ditto for gate fees, noise fees, peak-hour fees, passenger fees and overflight fees.
Space to park an unused plane isn’t usually an issue when it’s just one or two flights canceled; that will be included in some other fixed cost.

Lounges fees.
Scheduling coordination.
Administrative cost (managing/issuing tickets, etc.)

These are fixed (or step-variable), since canceling one or two flights won’t meaningfully change them.