Personally if Lexi has no problems with the crate at night I would leave her in it at night for a good while yet (just my opinion )
I agree! Coco was in the crate at night until she was a year old - she was a chewer and quite slow to get the housetraining lark 100%. She was quite happy in the crate so I carried on with it. Pups vary a lot so it is up to you to decide when she is ready to do without the crate.
With the housetraining, I reckon you need to get her out of the habit of weeing inside full stop ie get rid of the paper.
I think having paper is confusing for them as they learn that it is
sometimes OK to go indoors. I just took Coco outside every 30 mins or every hour until she was quite big and praised her every time she went. I have read that you should not expect too much on the housetraining front until they are a year old
You will just have to persevere and be consistent with her.
Good luck with her - sounds like she is doing fine so far