How to rescue exterior door paint job?
For getting paint off a door, I highly recommend using Citrus Strip.
We tried it on our old wooden door and it  worked great, taking off multiple layers of paint.  It doesn't work as well under a lot of sun and heat, so I would recommend either taking the door off the hinges or erecting some sort of tarp to block the sun from hitting it directly.  Then get a paint scraper,and it will come off pretty well.

For painting the door, they make small rollers (cabinet rollers) that we also used on our door, and it worked out very well. They are only about 4" wide.  I believe we used a latex paint, but I will check the can when I get home.