Just a comment on my method for the 1st part. As long as either n or n+1 or n+2 is a multiple of 13 and 19 is sufficient. Hence you can choose 37 x 38 x 39 where 38 is a multiple of 19 and 39 is a multiple of 13.

For question 7, there should only be 3 ordered pairs since 0 < m < n < 2008, which means (2007,2008) doesn't satisfy the inequality