Do you think this coat can be pulled off by a normal person like me, for normal wear?

Go for it - it's a beautiful coat and looks as though it ought to be warm, too. It's also jut about ideal for someone your age, build and religion - stylish, cly and not at all over the top. It'll go well with your headscarf, too - in fact, I've seen a few Muslim women wearing coats not dissimilar, and I think you'll look great in it.