I think your answer for 1) is fine. If you were to precisely apply the pigeonhole analogy, you could think of there being 30*33 total holes and 1000 pigeons, but obviously you understand the concept.

For 2), when you range from 0 to 3n, there are going to be numbers that are divisible by 3, and numbers that are not.

For instance, when n=2

0,1,2,3,4,5,6

0; 3,6 are multiples of 3

1,2; 4,5 are not

(notice the groupings)

I can supply a proof if you'd like, but it's intuitively clear and I don't know if you need it.

Once you know this, you know you have "holes", so you need "pigeons" before you are forced to pick a multiple of 3.