What are the brown stains showing through my white paint?
It’s tannin oil bleeding out through the paint. 

The first picture has a round (oval) shape that would normally indicate rust from a nail head. However, there is no blistering, so it can’t be rust. Tannin often will bleed out from knots. 

The second picture shows the brown-ish stain in a long linear pattern. This is typical of tannin seeping out of siding (especially Cedar and Redwood siding). 

All paint manufacturers recommend cedar and redwood should be primed prior to painting. Some paint types cover / block tannin better than others...oil based primers are best.