Several years ago, I had a job in which I was an assistant swimming instructor. I seem to remember that we progressed at about the same pace when teaching beginners, but now that you mention it, it does seem like an awfully rushed way of doing things. I mean, when there's a risk of people drowning, you would think that the people in charge of teaching the class would want to make sure that the students have basic survival skills, such as being able to keep their heads above the water, down. Still, if you managed to swim halfway across the pool on your first attempt at doing freestyle, you can't be doing bad. :)

Chlorine...what's a little bit of the "green killer", anyway? Really, though, you get used to it. I would, however, recommend that you buy some shampoo designed to treat Cl₂-damaged hair, though, if you don't want your hair to feel like straw. Anyway, good luck with your lessons!