You probably will want to back brush the coating on the deck. You can roll with an extension pole mounted to a roller frame, and just bend over to backbrush after the paint has been applied with the roller. You want to try to not work in the sun if possible and only do 1-3 boards at a time depending on how fast the material is drying. One coat is not enough if you are painting over raw wood. Two coats is best, even over a previously painted deck.

The fastest way to paint lattice is with a Whizz type roller. The Whizz is nice because one end is actually wrapped with the roller material so that you can get some of the edges while you are rolling the face. Work in small sections, use a brush to hit what the roller cannot and be sure to check the backside for drips as you go if that is a concern. Painting lattice is a chore no matter what, even for the pros. It is possible to spray it, but if it is cedar or something porous you want to backbrush/backroll for best penetration of the paint.

The best way to keep doors from breaking down outside is to maintain them. Perhaps coat them once per year. Also, prime and paint all sides, including the tops and bottoms. This will help to keep moisture out. Moisture is the #1 reason paint peels prematurely.