Sea Raider

If Sea Raider attacks a 3 power minion, killing it but also dying in the process, does the Raider have time to use their ability before they die?

Yes. After units are killed, there is time for effects to resolve (e.g. Deathrite) before minions are placed in cemeteries. This effect resolves in the same window of time as deathrites.

If I declare an attack against one target, but then a different enemy defends, does that satisfy this ability?

Yes. An attack was made, and then a minion was killed. As long as your attacking unit used the Move and Attack ability and then got kill credit, this ability is satisfied.