Board and batten should actually look physically realistic. Not obviously fake. Board width, no more than 12”. Then a 1 1/2” batten on top. Was the toilet placed far enough from the wall to add 1” of thickness and have it still mount?

shead- The horizontal trim piece is likely there to conceal a seam since I believe Hardie panel comes in a maximum length of 12'. My house doesn't have a trim piece on my two-story walls, but simply a small piece of flashing to handle that joint (which is painted the same color as the house). Either detail is fine, but I don't think the short, horizontal trim piece near the peak in the drawing is necessary, and the design would look better without it. Here's what one part of my house looks like with the flashing pieces:

Can you provide pictures? You want to use wainscoting to define the entry way, but if the areas don't already have definition, like a cased opening, you run into the problem of how to stop the wainscoting in a way that doesn't look awkward. In an older home with traditional styling, wainscot would end at a door casing (for example), not willy nilly in the middle of a wall (the step down may define the space, so for you it's not willy nilly exactly, but by itself it doesn't provide anything for the wainscot to run into).

Are you talking about the hallway wall (opposite the mirror), or about the back wall with the door? I ask because that hallway seems too narrow to lose any more width to hanging coats. The board and batten will add some thickness to the wall, and the bulk of any coats will take up more space. With the shallow cabinet on the other wall, it seems like the hallway would become uncomfortably narrow. Even removing the cabinet, I think with bulky winter coats you'd have less walking space than you have now. As to color, Simply White.