Well, I don't know of an in-universe answer to the Hair growth question (out of universe: the actor's hair grows and it's too much of a pain to keep it consistent.. and, of course, they like to change style, especially between seasons) but as to shaving.... By touch, like most men are stuck doing, from time to time.
Although a mirror is helpful for shaving, it's not mandatory; it can help you spot where you have missed, but careful shaving and examination with your fingers can do so as well. It's not as easy or efficient as looking in the mirror, but with practice isn't hard. And Angel would have had quite a bit of practice, assuming his hair still grows.
I'm 40, and having gotten tired of bothering with shaving with shaving cream years ago AND not being willing to bother with some kind of fog-free, in-shower shaving mirror, I've been shaving in the shower for about 20 years; it probably takes me a few minutes longer, but I promise, it's quite doable.