This is different for each of us, puberty happens at varying times and with varying degrees of development. Most of us probably start shaving around 13/14 but for some it could be earlier and for others a bit later. Facial hair and the hair that grows in other places (legs, chest, underarms etc) are also genetically driven so some of us are going to be more hairy than others. Height isn't effected by any of this so the two aren't related. The official end of puberty is age 21 although most of us are done with all of the development and growth by our late teens for sure.
There is no specific correlation between the two. When a guy stops growing taller, this does NOT mean he will next start growing facial hair. In fact, more the opposite is true -- facial hair generally comes first, growth continues into the late teens or sometimes very early twenties. Facial hair will develop more during this time, too.
If you suspect a growth deficiency, see a doc.
But don't worry about having each new thing happen at a specific time; everyone responds differently to the changes of adolescence.
I'm 24 and never developed facial hair. My puberty started right on time at around 13. I grew the most in height from 14-15 and gained a little afterward with a final half inch by about 18, maybe 19. Now whether I'M normal, well... But no I wouldn't say height and body/facial hair growth have any real parallel or that one necessarily preceeds the other. I had friends who started shaving at about 12 but didn't gain full height until 20-ish. And then again another friend shot up before any of us but didn't start shaving until 18.