|The Dread Pirate Hurley|
I don't know about the second one, but as far as the first and third go, here are my thoughts.
1. As written, you can't. He has no interest in you, and has complete faith in Mr. Plugg, who hates you. Making nice with Captain Harrigan is something you'd have to talk to your GM about. At one point later on before the mutiny there is a feast, and you might be able to make some progress with him there, but it comes so late it won't even matter.
3. Use your actions to influence crew members. The most important thing you can do is increase your friends and reduce your enemies, however you choose to do so. Make friends with Grok and Ambrose Kroop if you can. Either Diplomacy to make them like you, or Intimidate to make them afraid of you. If your GM rewards roleplaying, you can help NPCs on their actions or other things like that.
The first part of the game is a tiny sandbox hurtling down a railroad track. If done well, it can be a lot of fun. The status quo is that the officers basically hate you and there's nothing you can do about it but make nice with your fellow flunkies. Plugg and Scourge hate you, and you should probably hate them too.