@BobDDuck pretty much covered it but I am bored so...
FedEx boxes / Delta passengers, this one is easy.
There were times in the past where, in the same week, I would fly Delta, American, and United passengers. I've since changed bases and haven't flown passengers for anyone but American for months, however in theory I could pick up a United or Delta trip from another base at any time.
Loaders and ground crew work for FedEx. Are gate agents and flight attendants at regionals employed by Delta?
At hubs and larger stations ground staff may be mainline employees. in DTW and MSP the RJs were handled by DGS. In SLC the larger RJs were mainline, the 50 seater RJs were still contracted out last I checked. ATL has bounced back and forth over the years between contract and mainline depending on whether quality of service or cost was more important. I remember at one point having to do recurrent training on four different regional partners while I worked as a mainline gate agent. We had SkyWest, ExpressJet, Mesaba, and Compass all flying into PHX and all were ground handled by mainline employees. Podunkville is pretty much guaranteed to be contract employees.
Airplanes belong to Fedex. Same?
Depends. Delta owns or holds the lease on all of Endeavor's planes, same with those at Compass and the CRJ-700s at GoJet. They also own a smattering of CRJ-200s used by SkyWest as well as the CRJ-700s and -900s that they are taking from ExpressJet and moving to Endeavor. All told Delta holds the lease or owns a little over 350 of their connection carrier planes. Similarly United holds the leases to the ERJ-145s that are or were at ExpressJet, plus a fair number of their recent EMB 175 deliveries. According to the FAA data base American owns most of the planes flown by their wholly owned carriers plus some flown by independent regionals. It helps the whipsaw when mainline leases or owns the planes and doesn't have to worry about the plane getting repossessed for missed payments while shuffling it between regionals.
Airplanes maintained by Fedex. Same? Does Delta pay for maintenance on the CRJs?
Not directly, other than overhauls when shuffling RJs between carriers or on planes going in and out of storage paid for by the mainline owner.
Gates, ramps, facitilies - owned, rented, paid for by Delta?
Again, larger cities and hubs with mainline service, most likely yes. Even in larger cities with contract ground staff, it's not unheard of for the facility leases to be held by the mainline carrier. Two flight a day stations in rural areas, again, pretty much guaranteed to be owned/leased by the contract services provider as they are usually the only company there and provide services to all the regionals that fly in.
Does Delta literally pay money directly for regional pilot wages?
Arguably at Endeavor who's sole source of income is Delta, but not really.
Does Delta pay per diem, rental cars, hotels, and a plethora of other expenses for SkyWest pilots, for example?
Nope. I mean, only in the sense that Delta pays SkyWest and at some point some minuscule fraction of the money gets put into my paycheck, but Delta doesn't control what SkyWest pays their employees or provide any direct reimbursement for costs incurred by SkyWest employees.
