How was the colonial and early American experience shaped by British political turmoil and war, from the beheading of King Charles I in 1649 to the end of the Seven Years War in 1763?

That's an enormous question for anyone to answer without more details. What brings you to ask this question? We might be able to help more if we have a clearer direction.

As a starting place, I recommend you check out this open-access textbook for American history written and edited by college instructors: http://www.americanyawp.com/ In general, it's quite well-written and reflective of recent research.