First number 2: The integers are not open. Any epsilon neighborhood of an integer will contain points not in the set.

For number 1: I am not entirely sure, but you could try taking M such that Q is contained in M is contained in R. Suppose M is open. Doesn't this imply that M=R? (if M is open then for any point m in M there is an epsilon neighborhood around m contained in M. Use the density of the irrationals to show that M=R)