Hi Saffy
1. Yes she will get better at night. Remember she is in a totally new world with strange smells and away from her mum and brothers and sisters where she felt safe. Do a search on here and you will find loads of tips to try. The first one is to give her an old T shirt that smells of you as a blanket. A ticking clock in the room etc.
2. When she nips make a yelp like a puppy who has been hurt and she'll get the message.
3. It will be a while before she recognises her name. Make sure you do not over-do the calling, as too much and she will always ignore you. Just occasionally is enough at the moment and remember that you have to make yourself more interesting than what she happens to be doing at the time. Get down on the floor, say Molly Come in an excited kind of voice, clap your hands and make it so she wants to come to you, then lots pf praise and a reward for getting it right. One good tip is to have a toy which is looked on as yours, not hers - she will want it and when she has done something right play with her with it for a while, and after her little training session is over, put it away for next time.
Just remember it is VERY early days, and the first thing she needs to learn is to be sure of her new surroundings.

I have always shut the crate door at night, but do make sure there is something in it all snuggly, I usually cover all but the door with a blanket or sheet, it makes them feel more secure. You will have to get up early to let her out though.