Hmm, not really my period, but I'll take a shot at it...
1.
a. The Chesapeake would have been included in the colonial system managed and answering to the British. Indeed, the residents of the area at this time (at least the white ones) would have been considered British subjects. For anything more in depth than that you'll have to consult your textbook.
b. I'd assume the area was heavy into fishing. There was probably a lot of farming inland, and the various cottage workshops that supported the colonial societies of this time. This was pre-industrialization, so there wouldn't have been any heavy industry at all. Overall, everything would have been rather agrarian in nature. I'm not sure of the status of money at this time, or if trade largely revolved around a barter system. Again, consult your textbook. Also consult it for the role of slavery in said agrarian economy.
c. People would probably have been pretty up tight by our standards today, but living in something of a frontier area (could it have been called that?) they would probably been a little looser with their moral standards than back in Britain. This is just a guess. It's a safe bet that religion was very important in the community, and that strong family structures were highly valued. Also they would probably have been largely Anglican or of some protestant denomination. I'll bet drunken women were still regarded as sluts at this point in time, but try not to quote me on that. The families would have been paternalistic in nature. Not sure about choices in marriage or anything like that.
2. The answer to this depends on the cultures of the tribes of the area. They were probably more static than tribes from the western states, but maybe not as landed as white settlers. Their housing situation would have probably been more communal, with the women having more influence in the day to day operation of domestic life. If they were forced to adopt a more European mode of family life, the women would have been relegated to a role more akin to a domestic servant. There would have been less of a say for them in terms of family policy and the choices that were made in the day to day functioning of their basic social units.
3. White captives were largely integrated into the tribes and taken on as family members. This is not universal, but this is what generally happened. It stemmed from long traditions of integration of captives from other native tribes over the years. Indians taken into white society were probably looked down upon and forced to change ways to ascribe to white society. They would have been made to reject their own cultures, while still not being included as full members of the new culture that they were being required to take up. Many resented this, and would have wanted to return to their tribes whenever they could.
4. I have no good ideas on this one. It probably has something to do with the character of slaves from the different areas. Maybe the races of them. Maybe the slaves from the Caribbean would have been taken from established cultures there and were largely culturally homogeneous, whereas slaves coming straight from Africa were taken from many different cultures along the western coast and even from further inland, representing a more diverse group. The contrast of culture from the Caribbean to Africa would be stark anyway, but given a wide mix coming from Africa, you've got a melting pot of traditions, languages and beliefs all thrown into one group. That's my best guess.
All of this may be extremely off base, and could either be a good starting point for you or it could be leading you in the wrong direction. My best advice to you is to look this stuff up in the literature that your Prof has assigned, and to compare notes with the other students in your class. If you need, don't be afraid to go into your Prof's office hours and ask them to clarify things. That's why they're there.
Good luck!
