Sven has given you an excellent answer to both parts of your question.
I agree that different ways of saying the sentence about professional experience are simply an issue of formality. 'Haven't got' is more informal than 'Don't have', and 'a lot of' is more informal than 'much'. So, if you want to make the distinction between casual and formal use, I'd swap the expressions round:
'I haven't got a lot of professional experience' = informal/spoken
'I don't have much professional experience' = slightly more formal/written