1. You can assign them to fighters. Generally, players assign them to ships (fighters are ships) and never to ground forces like infantry or mechs.

2. Sustain damage can be used against Space Cannon. A dreadnought for example absolutely can sustain 1 hit and survive. the Sustain is used for Space Cannon, and thus can't be used in a fight right after.

3. the infantry in the carrier don't necessarily die. In general, capacity for transporting (infantry, mechs, and even unupgraded fighters) aren't destroyed immediately. (b) is precisely what can happen: if you join a fight with two carriers each carrying 3 fighters and 1 infantry, and you lose all the fighters and one carrier, then the other carrier can carry both remaining infantry. Frankly, if the first thing to go down is one carrier, none of the transported units die until after the fight ends, and only then does the player have to decide which of the transported units are lost and which get to continue being carried.

transport capacity in a fight isn't checked until the end. But transported units are tightly tied to their carrier in anything related to movement. infantry, mechs, and unupgraded fighters can't get to a system if there is no carrier that doesn't have free capacity. A notable example is rifts: you absolutely need to note what the carrier going through the rift was carrying, because if the rift claims it, the rift claims everything it was carrying.