Because you can't stain caulk? You may not even be able to paint it depending on the type of caulk. The reason you have gaps primarily is that the framing/drywall work is poor. When there's a color change like light walls to dark stained trim or whatever, the gaps are less noticed than when you have white trim on a white painted wall.

zobeet, The FPE primer will be fine as long as it's covered with paint. Peeling and other issues are caused by dirty surfaces, moisture penetration from backside, etc. If you prepped the surface properly, the primer will not cause any disappointments. Paint over the waterbase with at least 2 coats of quality acrylic paint. Michael

I have several questions. First, are the nails galvanized or stainless steel? If they are galvanized, I would prime them first with Ospho before caulking and then prime with a regular primer. Ospho is a green liquid that will turn rust black and prevent bleed through on your paint. Galvanized nails rust fairly quickly and this will head off a problem in a year or so down the road. You can also use Hammerite Rust Cap Primer for the nails. (Many painters tell me that QTips work great for applying Ospho). If they are stainless, I would caulk first and then prime the surface. This will prevent any flashing effect from the Ospho on the finish coat. I would actually prefer to use a spackling compound that will stay somewhat flexible, but you can use caulk also. Is the siding a hardi-panel or hardi-plank? I have not seen any real wood siding pre-primed in my market. If it is hardi-plank, I would prime the siding with a good latex 100% acrylic primer. You could use 123 by Zinsser, Suprime by Pratt and Lambert, or FreshStart by Ben Moore and then topcoat with your choice of paint. Every paint company will manufacture a 100% acrylic primer to use with their topcoat. The primer used on siding as well as steel doors is to protect the product in shipment. It is still intended to be primed before painting. I would highly recommend that your primer be manufactured by the same company as the paint for warranty reasons. Make sure you use a really high quality caulk. I have found that Big Stretch Caulk by Sashco is the easiest to work with of all the caulks on the market. It is paintable. It is a little expensive, but is very flexible and smooths out great. Consider having your primer tinted 1/4 to 1/2 formula of your topcoat color. It makes the paint cover better. The primer will still be a little light to the finish coat so you can see any areas you have missed when applying your topcoat. I do recommend two coats of finish paint.

I can answer most of your questions, but not #2. You do not need to reprime the doors, just sand lightly with a fine sandpaper or sanding sponge and vacuum off the dust. Sand lightly between coats of ProClassic and vacuum dust. Drying time depends on humidity. Personally, I like to wait 24 hours before recoating. Refer to directions on paint can. SW carries Purdy Chinex brushes - at least mine does. If you have time, you can order Corona brushes online at thepaintstore.com. That's were I got my supply of them.