Actually, I never apply primer to my body, or any of my parts……
I use primer only to find surface defects in a near completed model, or under colors such as white, yellow, orange, and some reds.
If the paint scratches off, the surface wasn't properly cleaned before it was painted.
Some paint on the sprue, some paint off the sprue. Generally, off the sprue is less work, but not always.
Whether you paint before or after assembly depends on what is easiest and most efficient. Sometimes its best to paint some things before assembly, especially small parts. Sometimes not. Which depends on your plans for assembly.