I would also suggest to match the walls. When you look at where the stairs meets the wall...by making it two different colors it will appear choppy looking. Making it blend in together like it is part of the wall won't make that corner and the stairs stick out like a sore thumb.

Your mockup scheme is similar to our master bathroom we just completed - photo below. I know you mentioned storage being a concern - our mirrored cabinet has offered an amazing amount of storage in a very small space and also helps bounce light around. I was worried about black taps etc too so we kept chrome fixtures but added in a matte black candle and black potted orchid to create a similar effect which we can change out later on. Our floor tiles are dark but because they are semi-polished they actually bounce around a lot of light and don't make the room feel dark if that is a concern. We also have a huge fiddle leaf fig in the corner (not pictured) which adds a really nice feel to the space - a plant like that could help bring in the outside greenery in your bathroom. Instead of the storage tower you have to the left of the vanity could you do say some floating wood shelving, possibly with baskets added for more hidden storage? You could also bring in the 60s theme with what you displayed on there eg. photos as you mentioned? In regards to the window - a previous house we lived in had a window at about shoulder height in the shower - as well as letting in heaps of light it was amazing for storing toiletries etc!

Dulux whisper white. Get a sample pot, paint a large piece of cardboard and see for yourself.

Really hard to tell. I like the lightest one but I'm not very adventurous. You may need to choose one and paint a larger area and see what you think.