Wow, you sure ask a lot of questions
1 Advantages to mechanicals is they are more dependable, require less maintenance and are much less expensive, but air retracts are easier if you have a nose gear. The best type of air retracts are subjective, but if you lose pressure, it's nice to have the ones that spring down in case of pressure loss - of course, they're even more expensive.
2 Rotating retracts are for planes where the gear retracts rearward and the wheel rotates 90 degrees to lay flat inside the wing. These are only used for scale planes where the full-size plane had wheels that did that (Like a Hellcat)
3 Steering linkage is done with a pull-pull setup (See pic)
4 Not many people use gear doors due to their complication, but they can also be actuated mechanically or pneumatically. In either case, there is usually an electronic synchronizer to sequence them.
5 Retract servos are necessary for mechanicals. They need the extra torque and the slow movement gives them a scale look as they transition. For pneumatics, a standard servo is used to actuate the air valve.
6 Mechanicals only need to unplug the servo from the Rx, pneumatics only need to unplug the 4 airlines. If you have a mechanical nose wheel, it will need its own servo which will stay in the fuse when the wing comes off.