At first when you said 2x a day, I started to think you were doing too much, but honestly it doesn't sound like you are. You're putting in about an hour a day which is reasonable.
It *is* normal to sleep better after exercising. I find that when I exercise regularly, I don't have insomnia problems and my sleep is deeper and more restful. And I need less of it.
And also when you first get into it, yeah, I think you'll feel more tired at first. Your body is adjusting to something new.