I'm curios if you've got any interest in the manga? It would cover a lot of those details the anime zips through, as it's sort of expecting people to know the story (at least up to a certain point). It's REALLY GOOD. ♥

Also, I think the reason Ed doesn't stop being a State Alchemist is that he signed up - and once you join an army, you can't exactly quit just because you get bored. There's more than just insult behind the phrase "Dog of the Military". Quite possibly he's now bound by a contract way stricter than you'd find in any civilian job.