Yes and Yes.
Fighters on a carrier always defend.  Even if your fighters are on my carrier, they still defend if we are attacked.  However if I am the instigator of the attack and move my carrier into combat with your fighters on it, then your fighters do not attack, they are considered cargo on my carrier.  And if my carrier is sunk, the fighters are sunk with it.
As for transports, yes your posted move is legal.  Remember the following rules:
1. After you unload units from a transport, those units may not move any more this turn. (ie. a tank may not unload, then move a space).
2. After a transport unloads units, the transport may not move any more this turn.
3. A unit may not load into a transport if it has already moved this turn (ie. a tank may not move a space, then load)
So basically a transport may load then move then unload in the same turn, but it may not unload then load because unloading ends its turn.  Hope that clears it up. (like mud)
(edit: Baghdaddy beat me to it!)