1) Copies of the passenger lists are available on FamilySearch.org, so you can review them to see if they have more info than the transcription. But for that time period, there probably won't be much more than what the transcription shows.
2) Since they arrived and left in between censuses, the next best source of occupation info would be the city directory for wherever they were living. The availability of city directories is kind of spotty prior to 1861, but Ancestry.com has copies of most of them. The city directories generally only list the head of household.
3) No. Passenger lists were not required for leaving the U.S.