Is it normal to feel regret?

Yes to all your questions, it's perfectly normal and a part of the process of learning about each other and understanding each other's habits and beliefs. I actually find it one of the most exciting periods of a relationship because you discover something new every day if not every hour.
It's normal to be unsure, and both of you will just have to find your own comfort zone. And if you are really not comfortable with him after a couple of months, well then there are always other guys around.

Yeah of course there's always doubts in a relationship at times. But if the feelings are occurring a lot, and they're really strong. Then you should probably re-evaluate your relationship and how much the other person means to you. If you decide that neither are important then you probably shouldn't be with them. Its just wasting your time, and leading that person on if they really like you which isn't fair to them and its not fair to you because you could be with someone who you really like instead of. If its new though maybe you should get to know the person a lot better, have deep conversations with them. That always helps you figure out the person they are and that can answer your question about if you like them really.