Your P-38 escorts and C-47 transports can only be intercepted by a single Axis fighter:
The player can intercept with a single Active Fighter (never more than one) with a Patrol Zone into the mission hex.
So the Axis player in this example only gets one shot at intercepting the mission.
Interception is then resolved as Air Combat.
The rule on Air Combat is 14.3.
14.3 Air Combat
When both sides have Active planes in a hex, Air Combat is immediately resolved. This will only happen when the mission hex contains an enemy air base with Active aircraft, or during Interception (14.5). An Air Combat consists of a series of rounds during which each player selects one unit to use. The result of the round may be the aborting (see 14.1c) and possibly a loss to one or both of the selected aircraft. These rounds continue until one side or the other is alone in the hex (or no Active plane with a non-parenthesized Air Combat Rating remains).
So the single Axis fighter starts by fighting a round of Air Combat against one of the Allied planes (Allied player choice).
The Allied player will obviously choose one of the P-38s to fight the first round.
If the Axis plane aborts, it heads back to base inactive and the original Allied mission continues.
If the P-38 aborts and the Axis plane does not, another round of Air Combat ensues, between the same Axis fighter and the next Allied plane, very likely the second P-38.
Air Combat continues, single plane vs single plane, until either the Axis plane aborts or all four Allied planes have aborted (which would usually only happen if the Axis won four rounds of Air Combat).
The answers to your questions are:
1. If the Air Combat results in an abort, does the entire mission abort?
2. If the entire mission does not abort, and other aircraft attempt to intercept the mission?
3. If the first roll does not abort the mission, can other aircraft attempt an intercept?
(Edit: beaten to the punch by the much more succinct TankBoy)