1. How many servos in total will you be using? The ability for the servos to run with enough force will largely depend on how they are being powered. For electric RC car applications, power is generally provided from the Electronic Speed Controller (ESC) through the Battery Eliminator Circuit (BEC). The current available in this BEC will determine how your servos run together. It is possible to buy an external BEC which allows for more current and connector directly to the battery, but then it is necessary to disconnect the power wire from the ESC's receiver plug so you aren't feeding in too much voltage.
2. All the numbered channels on the receiver will output a PWM signal. Typically for electric cars we power motors with electronic speed controllers, I'm not familiar with the PWM boards you mention, perhaps this is a robotics thing? How many motors or servos in total are you working with?
3. I believe you can provide power to any of the sets of pins on the receiver, so if you do use an ESC this will provide power to the receiver and the rest of the channels. If you aren't using an ESC, you can connect a battery to one of the pin sets instead.
4. Not sure about legality, but usually there are design difference between air/surface radios. As you mention, the Radiolink receivers are advertised for ground and air, with a shorter range listed for ground use (500m). Usually aircraft need more channels and compact, lighter receivers. This leads to the in-line receiver design like your R8EF. The T8S looks to be designed primarily for drone racing, but if you need all the channels and the layout suits you then I don't know any reason not to use it.