Aww, congratulations on your new baby
Yes, they will cry at night and keep you up until they get used to staying in their crate or pen. I kept mine in a crate right next to my bed and whenever she cried I told her 'shhh, time to sleep' and I'd stick my fingers through the gate and she would fall asleep leaning on them. You can put an article of your clothing in there with her so she can smell your scent.
As for the spurts of energy and climbing all over everything - yup, she's right on track