How to handle a puppy crying in the crate at night
I understand why you are hesitant to take her out of the crate at night when she cries. We don't want to reinforce the crying, but at her age she will need to eliminate during the night. I would make sure she has eliminated before putting her in the crate and make sure she is tired. If she sleeps for a few hours and then wakes up crying, definitely take her out to potty. When you put her back in the crate, if she cries, just ignore her since you know she does not need to potty. At her age (2-1/2 months), you could assume she could hold her bladder about 2-1/2 or 3 hours, so you may need to get up once (or possibly twice) during the night. I would not withhold food from her for not eliminating. Feed her at your regularly scheduled times (2 or 3 times per day).