Spray vs. Roller and Brush
For outdoor jobs you can only spray on a perfectly calm day. Even at that, you are going to have some overspray on the shingles of your roof, so be prepared to cover everything to keep the overspray off. To spray the inside of a home it has to be unoccupied because you can't cover the inside of the home well enough to keep the paint off of the contents. Inside rolling or brushing is typically the best, and if you are doing sheetrock walls, roll the paint (and not like you see on TV where they are going every which direction). When you are putting the paint on, apply it in up and down rolling strokes, and then come back and start at the top and pull everything down one row at a time in order to pull all the sheen in the same direction. Remember, if you are using a semi-gloss or a gloss, the glossier the finish the more important it is to pull the paint in the same direction with all your finished strokes, so you have it all pulling for the same sheen.
How to use painters tape
There are several different types of painters tape each designed for different surfaces, so match the right tape for your job. The adhesives are all heat activated. When you put one along an edge keep it nice and tight. Then make sure you take your finger and rub all the way down rapidly, so you generate some heat to seal that bond; otherwise, the paint will actually leach underneath the tape. Once you are done with your painting, you need to make sure to remove that tape while the paint is still somewhat tacky. If you wait until it's totally dry (like a day or two) you are going to have a rough edge because some of the paint will come off with the tape. If it's still a little moist, you are going to have a nice clean edge.
Purpose of primer
Primer soaks into the material and seals it providing a clean consistent surface ready for paint. Without a primer your paint will get absorbed into the surface. Sheetrock, for instance, has a paper on the outside of it, and will absorb the paint and change the sheen of your paint if you haven't sealed it with a primer first. Don't be fooled into buying a "primer-paint-in-one" thinking you can skip a step. That is only fine if the walls are already painted with a similar color. If you have a bright red wall and you are wanting to go back to a light color, use primer sealer on it first or you are going to repaint that wall several times.
Peeling paint on trim
If trim paint is peeling that means oil-based paint was put over a coat of latex paint. Oil-base will never stick to latex paint, and it will start peeling off like a rubber glove. I hate to tell you this, but the only cure is to sand all the paint off ...strip it down and start from scratch and even then you may have some issues. Typically in that situation you are faced with sticking with the latex paint, or replacing the trim.