I'm pregnant and my mom may need chemo soon. Will she be allowed to hold the baby?

Most likely. There shouldn't be any danger to your baby after grandmother has chemo. However, if she doesn't have a functioning immune system because of the chemo then the baby may pose a danger to her. Follow the recommendations of her oncologist (cancer specialist) with respect to when she can be around the baby. Usually if the baby isn't sick or hasn't had certain shots it should be fine.
Yes. Unless your baby is sick, in which case being near your child may jeopardize your mother's health, there is no reason why she shouldn't be able to hold the child. Moreover, psychologically it may give her a big and needed boost. Chemo can be hard.