Our cottage kitchen base cabinets are Ikea but we're using a local company for the uppers to allow more customization. I have a concept drawing from the KD and for the most part I like it. One (second picture) wall is completely without uppers and I would like opinions if the shelves should be on that wall as well.

Your space is gorgeous. Since you don't need the extra storage, I would keep it very simple and place a few black-framed prints on those shelves. You can go black and white or use pop of color, vary the sizes, and overlap them to add interest. I'd also mix in a little greenery and wood elements, like a couple oversized cutting boards, to warm it up and tie in with your floors.

The shelves appear to be sitting on the carpet so there isn't any reason to wait to remove them. I would carefully disassemble them, remove the nails & salvage the wood. I don't think they are going to remove as 'units'...look to have been built in place. At least, the narrow shelved part will need to come out in pieces. The longer, double unit may come out whole. That lumber will be useful for any number of things. Not the greatest quality in some of the boards because of the large knots but worth saving to use for shelving in the garage, basement, closets, storage shed, etc.

I think the mirror can work if everything else is kept simple, with touches of gold to reference the mirror frame. I'd paint the interior of the medicine cabinet the same color as the walls. You could do glass shelves or the same material as your vanity countertop. Your shelves look nice and deep; they'd even be good for a person to set their whole makeup or toiletry bag when staying with you. Especially if more than one person is using that bathroom, the vanity doesn't offer a lot of storage space. Alternatively, you could have fun in this room and go maximalist with wainscotting and wallpaper or a fun trim color and wallpaper, still keeping the mirror. If you're moving electrical anyway, is there space to scootch the vanity closer to the toilet a bit so you could fit a slim sconce on both sides of the mirror?