Yes, but your cell tower aren't moving around relative to each other. And in order to get the data rates that they need at the speed they need, the signals between the satellites will be more focused rf or laser communication. So all of the satellites have to constantly know which satellite is closest to them and how to point antennas and/or lasers.
Yes, but your cell tower aren't moving around relative to each other.
Depends on the observer. If you move in a circle around a set of radios (driving around town) either you're stationary and the other radios are spinning or vice versa. Also, many satellites will share the same orbit, they will be stationary as far as each other are concerned.
True, the satellites within the orbital plane will remain close to stationary to each other. There will be some perturbations, but generally will be stationary relative to each other. In one of the plans I saw floating around the inter-satellite links within the orbital plane will basically be stationary laser links between the satellites. And the cross-links between the orbital planes will be done with phased array antennas so they can be electrically steered instead of physically steered.