Feeling exhausted is very normal. You will likely feel this way for most of the first trimester.
Yes, it's totally normal. With a few of my pregnancies, I struggled to do anything but sleep and move to the couch to sleep more. I was young with my first, and I remember going to bed at like 4pm- just to wake up still exhausted the next day.
Some cramping is normal too- if it gets worse or is accompanied by bleeding, go ahead and call the doctor to have it checked out.
Congratulations!