The two definitions needed are as follows:
According to 11.4,
strategic Air Movement must start and end in Friendly Territory and may not pass through Neutral or Rival/Enemy Territory (i.e., AFs at Sea or in non-Friendly Territory cannot use Strategic Movement).
According to 13.0,
ReBasing is making a free move (no Command needed) during the Combat Phase out of a Disputed area into an undisputed friendly-controlled Land Area.
And from the brown box on page 16:
ReBasing: Double Movement Range
ANS units can effectively double their movement range in 2 ways:
• Strategic Movement. They can double their normal movement range within friendly areas (provided they do not Engage or Disengage).
• By ReBasing. They can move normally into a Battle and then move out of it again to ReBase (effectively doubling their movement range).
Note that both these cannot occur on the same move: ReBasing is movement out of a Battle, but Strategic Movement is not allowed into a Battle.
The answer to Q1 is No, they cannot.
The answer to Q2 is if the AF units both decide to ReBase after combat has been resolved during a Combat phase, then they both simply fly home without additional combat. See 13.12. The key word is "after."