Axis & Allies Developer and Playtester; War of the Ring Editor and Playtester
If France mobilizes Portugal on turn one with a INF on a transport, can France send other transports to pick up the Portuguese troops immediately and land them elsewhere (e.g. in Spanish Morocco?)
No. From page 12 of the rulebook:
All mobilization must be done at the end of the movement phase, after all movements have been completed. The only exception is if a minor power is being mobilized as a result of an amphibious assault or reinforcement (see “Amphibious Assault and Reinforcement Movement”, page 17) that involves a sea battle. In this case, the mobilization is done immediately before the moving land units are offloaded into the territory.
When attacked, mobilized units (Serbia) fight defensively immediately, but can they likewise act offensively?
If they survive the attack, yes.