I have yet to have an alarm clock onboard cruise ships, but its very easy to have a wake-up call if you need, works wonderful! I'm also fortunate with short hair that the hairdryers onboard do work out well for me, but if you have real thick, long hair, may-be bring your own would be better.
Yes, the Pride has hairdryers. They're connected in the drawer in the desk. Believe it or not, I never even used it. I have pretty thick wavy hair, but I always air dry it, even in the Caribbean. So, sorry, I can't tell you if it's any good or not!
As for the clock, the answer is no, but you can set up an automated computerized wake-up call on the phone system. We couldn't (they didn't have it up and running yet on our maiden voyage) but you can. I remember reading someone's post since then that siad it's working now. The TV has the time, too. I think it was on the channel that shows you where you are, with the ship's speed and all that.