Ha.

Right

で indicates something you use, and so is often translated as "with" or "by". E.g. 筆で書きます　（ふででかきます）　"I write with a brush", or 電車で来ました　（でんしゃできました） "I came by train".

You generally have quite some freedom with how to order noun/particle combinations. Switching order should be no problem here.

I answered in that order and it was marked correct. However, i can see further down the comments, user Trissie suggests that order is important in this case. Google translate backs that up; I plugged in とけいをお金でかいます and got "I will charge money by watching".