Oxylic acid will remove rust stains. Zud contains oxylic acid. Buy the Zud in the squirt bottle not the powdered spinkles. Let it sit on the stain - like a whole day. You do not have to rub. Then rinse. You do not say whether the stains are only in the glaze, or if the glaze is crackled and the stain goes deep into the porcelain. Stains in cracks, of any type, are going to be more difficult to remove.

My mom taught me how to deal with rust stains when I was a kid ( I have loved laundry since I was in diapers). Simply, wet the rust stains throughly with lemon juice, then rub table salt into the stain. Place the stained item directly in the sunshine, preferably laid flat out in the grass. Give it a few hours or so. You might have to repeat it once more, depending on how badly the stains are set, and how heavy the stain is. I have never had this NOT work, even on some old clay dirt stains. Commercial rust removal products do work, but I have less experience with those on individual stains, only whole loads of rusty whites.

Shower door crevices are difficult to clean. I start with Liquid Comet Bathroom Cleaner, leaving it on for 10 minutes, and then scrubbing with the rough green side of a Scotch Brite scrubbing sponge and then rinsing. If you see an improvement, you know you are on the right track, but you may need to repeat it a few times. People make the mistake of using these products without letting them set and do their job. Set a timer for 10 minutes so you are not tempted to mess with it too early. Another thing that will work but is not recommended because it can damage the aluminum, is a solution of TSP and water. I have used it on old aluminum windows and it cleaned them well. Don't let that sit on the metal, though. On the marble/cultured marble, until you know what you have, you might want to try using a razor blade scraper to very carefully scrape the gunk away. You want to be careful not to gouge the marble, but with some skill, you can get the blade at just the right angle and scrape off the junk. And yes, a canister steamer is great in a bathroom, especially for getting into the crevices. You might want to google "how to tell the difference between marble and cultured marble."

You can use a stripper, such as Citristrip. Google for lots of step by step instructions people have posted of their projects. Wear thick gloves and keep steel wool or any kind of steel brush away from it. I just did a coffee table and nearly ruined the entire project using steel wool to remove the stripper from some tight areas. Long story. :D You’ll possibly still need to lightly sand with a fine sandpaper, depending on how well the stripper works, and to clean it up. I’d try a 220 grit first, you may have to go lower. Have a couple of old toothbrushes handy for around the nails. Clean it all well after stripping/sanding and stain again or just seal the natural wood with wax or a water based poly. I just saw this tutorial using Citristrip spray. I’ve never used the spray, but it might be worth looking into for a small project like yours: https://www.pineandprospecthome.com/citri-strip-spray-honest-review/