G' Day BKerins,
Sorry for the delay; my Internet has been down for a couple of days due to the rain in SoCal.
Sounds like you've pretty well got it, but here are the answers to your original questions to ensure we're on the same wavelength:
1. Aircraft can move up to their max Clean/Loaded movement each AP, except when taking off or landing. Section 2.5.2 Taking off is limited to 1/3 of the aircraft's Clean movement to simulate increasing speed from stationary to flying speed and climbing to Altitude Level 1 in the take off Air Phase. Similarly, landing is reduced to 1/3 Clean movement in the Air Phase landed to simulate the deceleration from Altitude Level 1 to a full stop on a carrier or runway. Section 2.5.5
2. The distance moved in other Air Phases can be any distance desired by the gamer up to the aircraft's maximum Clean/Loaded distance. This maximum horizontal distance is decreased by a climbing decrement (Section 2.5.3), turn decrement (Section 2.5.2 or expanded by a dive increase (Section 2.5.4). Thus, you can move flights straight part of an Air Phase to gain some distance from the carrier or airfield and spend the rest of the Air Phase circling for aircraft to form up. Generally, forming up would be done in sight of the carrier or airfield, but a reasonable distance away from to to avoid hindering other aircraft taking or forming up. These forming up movements would also be decremented for increasing the altitude of the formation. When unopposed, this can be assumed to be completed in a couple of Game Turns (each 3 Air Phases) to allow all aircraft in the formation to take off and form up without having to go through the details of each Air Phase's movement. The time needed to form up and fuel burned was one of the reasons strike groups didn't assemble into just one giant formation. The take off and landing details are provided primarily for those situations where aircraft are taking off or landing during an attack by opposing aircraft. Then, the take off and landing Air Phases can become quite critical as the aircraft are sitting ducks in the event of opposing firing passes or strafing attacks.
In answer to your question about how many "rounds" strike groups need in transit to their targets, you will find that is covered in Section 4.5 which deals with air ops beyond the tactical battle area of one side's carriers or airfield - which was, of course, the normal situation in WWII. In this context, the rules in Part 2 cover the detailed, tactical air ops in the immediate vicinity of a carrier, airfield or task force while Part 4, Campaign Ops, covers air ops to scout for opponents and getting to and from the tactical area of opposing task forces and target areas. In effect, carrier battles are mini-campaigns that take place in one day most of the time. You will find the bottom of the Formation Cards contain the data needed for ranges and movement between Campaign Hexes which simulate the distances involved. Further, Part 4 also contains streamlined procedures for resolving searches, aerial interception, air attacks and AA defense for those don't want to spend a lot of time simulating all the tactical details of those activities. You can choose to use the Part 2 detailed procedures for tactical attack resolution in the target hex or the streamlined Part 4 procedures as your gamers prefer.
I would add that there are few things more nerve-wracking than sitting around with your team while the referee determines which side spots the other first or you have to decide whether to launch and hope a contact report comes through to get a jump on the opponent or decide to wait until your scouts find them. Very much like the tension real commanders had to go through. Carrier battles are usually quite exciting for both sides.