How do I know if I'm thru puberty? I am 25 years old and barely have facial hair. I still even get the random erections for no reason.

Physical exam. A doctor can evaluate you to make sure you have completed the changes of puberty but by 25 years of age you should definitely be done. Facial hair volume is a matter of genetics, some men have very little hair, some have a lot. As far as the erections, part of becoming an adult male is learning how to better control them, it doesn't mean they stop happening or go away completely.