Jay is pretty much right on. Kiltz is a must. I would lightly sand first as he said. If there is any mildew showing then hit it with a mild water and bleach solution first, rinse and let dry. The kiltz is so good that you shouldn't have to put two coats of it. If the pink still shows after one coat you might want to use a second of kiltz instead of your finish paint b/c it has much more pigment and covers better. Make sure you stir the heck out of it first. Also, flat paint is not a good idea in the bathroom. I re did my bath ceiling with white paint that was something just less than glossy. Not glossy, not flat. Flat will not resist the moisture well enough and will not hold up well with cleaning or if mildew gets to it. A satin or semigloss is much more moisture resistant. If you use it, you may want to touch up the spackling of your existing ceiling b/c blemishes will more likely show up with a non flat paint. If you do this do it in between sanding the pink stuff and your first coat of primer on in between coats of primer. Paint stripping (the door) makes me retch. THere is no less pleasant thing to do in my book. I would either bite the bullet and get a new door or just paint it white and deal with it. Once the pink is gone, you won't even give it a second thought. Naturally finished doors I think are overrated. Good Luck!