If that floor is pretty stable you might be able to just put shluter right on the pine and save some height.
You can not install Ditra, or any other membrane or concrete backer board over plank flooring. You need a plywood underlayment first. If those 2x4's are perfectly flat you can go with 1/2" B/C exposure 1 ply, otherwise you will need 5/8 or 3/4".
Tile is not gonna make the floor waterproof, although bathroom floors are not usually waterproofed.
Make a wood or marble threshold transition in the doorway.