A. Yes, this can be done fairly easily. I have done several over the years. Preparation is the key here and if steps are skipped, the quality of the end result will be substandard.
Step 1. Sand the entire area to be painted with 320 grit Sandpaper [link is to product info at Rockler], you don't want to sand through the gel coat you simply want to sand until it hazes over and the finish becomes dull.
Step 2. Clean the shower with Muriatic Acid [link is to product info at Amazon] to remove all of the dust. Then rinse the entire thing with water and let dry completely.
Step 3. Painting. Use a good quality primer first then use a good epoxy based paint in the color of your choice. Rustoleum makes an "appliance paint" which work perfect for this application.. The only draw back is the only colors are white and almond. I have used oil based paints before as well with a satisfactory result, you simply have to watch close for runs in your paint. Always use a spray gun or spray can, never brush or roll paint on.
That's it, its really that simple and the results are usually stunning.
Good luck!