If my UK visa gets rejected, would it affect my Schengen visa?
It depends on the reason for rejection. If its a good reason (say, lack of funds), that you havent been able to address in the intervening time, then you will most likely be rejected again. If its for something relatively trivial (spelling errors, mixing up dates, that sort of thing) then it might. Give your side of the story in your cover letter and they will probably take it into consideration.