I don't think that British rule would be as repressive as some people are suggesting. Britain simply lacked both the resources and the desire to place the Thirteen Colonies under permanent military occupation, so any plan which required ongoing massive repression would be a non-starter. The most likely peace settlement, in my opinion, would be either (a) the Colonies are directly taxed, and in return get representation in Parliament, or (b) the Colonies have to pay a contribution towards Imperial defence, but they get to choose how to raise the money themselves.
I don't know, the South was historically more loyalist than the North, wasn't it? Plus, if the general trajectory of history goes at all as it did IOTL, Britain will soon be reaching the height of its power, so it's not likely the southern and middle colonies would be able to win a War of Independence Round 2.
If it gets to war and defeat, it's likely all or some of the colonies would rebel at a later stage, depending on how the British handle matters. Places like New England and New York would likely forget memories of the war due to ongoing immigration, but the rest would nurse grievances and are growing in power all the time. It's possible you would have a bit of a balkanised system, with sectarianism meaning independent southern and mid-Atlantic states, with British dominions in the north.
I don't know, the South was historically more loyalist than the North, wasn't it? Plus, if the general trajectory of history goes at all as it did IOTL, Britain will soon be reaching the height of its power, so it's not likely the southern and middle colonies would be able to win a War of Independence Round 2.