Whether to cook the wings with the marinade, or apply it after cooking depends on your specific recipe or method. The traditional technique for Buffalo style and similar wings is to fry (or bake) the wings sauceless, and then toss them with the sauce after cooking.
The advantage of this method is that you will not burn the sauce (which if it is sweet, can burn easily); the disadvantage is the sauce does not cook onto the wing, and so how well it adheres is down to the thickness of the particular sauce you are using.
The other traditional method, more often used for grilled wings or baked wings is to cook the wings until they are mostly done, then baste them with the sauce for the final part of the cooking. The advantage of this is that the sauce will not burn, and is baked on to the wing. The disadvantage, of course, is that it is more work.
There is no simple answer to getting the sauce to stick to the wings. The biggest influencer is the thickness of viscosity of the sauce recipe itself, so that it sticks of its own volition.
There are many methods that result in tender meat but crispy skin. Perhaps the three most common are:
Baking. Baking is relatively slow, and so makes it easier to cook them without overcooking. Alton Brown, for example, recommends 40 minutes (with one flip) at 425 F / 220 C.
Deep Frying. Deep frying can cook them through and render the skin very crispy, but is very fast, so it is harder to prevent overcooking, and more sensitive to size variation among the wings. The Food Network recommends 375 F / 190 C for about 15 minutes.
Steaming (or otherwise par-cooking) the wings to cook them through and render the excess fat under the skin, then crisping them with another method. This is most often done when doing a grill (in the sense of a charcoal grill) to finish. Serious Eats uses this method solely on the grill, initially cooking on the cool side of the grill to cook through, and then searing on the hot side to crisp up.
Whether to use a rack depends on the cooking method; it only is applicable to oven baking, where it is a good idea.
Oil is not usually required for chicken wings, which have a great deal of fat under the skin. Normally the challenge is rendering that fat.