Here's an article on painting aluminum doors: https://homeguides.sfgate.com/repaint-aluminum-door-25657.html
Yes, but you must use an aluminum based paint. This will withstand the moisture and adhere the best.
There are many types of aluminum primer to use after you have prepared the surface. They all work better than smearing paint on the slick surface of aluminum. You can choose to roll on, spray on or brush on a professional aluminum primer. , let dry, then sand again. https://www.amazon.com/SEM-39683-Grey-Etching-Primer/dp/B000GTIRAU?ref_=bl_dp_s_web_3041192011
4.Apply paint (multiple coats, and sanding between coats, may be necessary).
5.Apply enamel sealer.
Yes use rustolium paint
I used spray paint on a table top rim, and the paint peeled off. My second attempt I lightly sanded the surface and used a primer first. This worked well.