These chairs are easy to recover and the range of fabric available today gives you plenty of choice. I say go for it. If you don't feel up to it yourself get an upholsterer, but plenty of YouTube tutorials about.

Something to take into cosideration would be the amount of light you have coming into the bathroom. Obviously if you have considerable light and air the tile shade wouldn't be too much of an issue. On the other hand if the room is small and not very light filled, then the lighter shades would be preferable giving the illusion of making the room appear bigger and lighter.

Once you go white (which I think is a great idea) you might find that the existing handles look good. If you want to change them I would suggest handles that are consistent with the period of the house/kitchen. And, I would keep them simple based on the design of the cabinetry. :-)

I was thinking maybe a pergola so that you can still enjoy the sun when necessary but have a small area where you can just relax with your family. What were you thinking?