Most of the time you will not see any evidence of a chinchilla being in heat. Occasionally, a female will have a slight, clear discharge from her vagina.
As far as the pee stains, that happens quite often. Some chins will sit in their pee and that is what causes them. You can try cleaning the area with a unscented baby wipe and then giving the chin a dust bath. It may or may not remove the stain.