It is alright for women to cut their nails and remove the pubic hair in the state of menstruation, though it is not good rather it is makrooh tanzihi. You may cut your nails and remove the pubic hair as and when required. It is mustahab to throw the fallen hair in any clean place or bury somewhere. It should be noted that if by cutting the hair you mean the hair of head then it is not allowed for women to cut the hair of head.
Allah knows Best!
Darul Uloom Deoband