If you can get or build a small shelter or shed for the washing machine you'll likely be glad of it. It would take up valuable space and produce noise in a caravan.
I can't think of a reason that 100ft would be a problem for water or electric, assuming the wires/pipes are suitable spec'd and installed.
We were about 80m away, which was good. Wouldn't want to be really close, but depends on the site etc. Big lorries, diggers, things falling off scaffolding need to be considered. And if you have kids, that's another factor.