If the woman did this while not being aware of its being wrong, then this does not affect the validity of her prayers. If she was aware that it is not legislated and insisted on doing this then the prayer is invalid.
Performance with the same sex is not accepted in all religions. People who are infected with this problem should seek cure to it so they can live a healthy life. Submission to the right to practice such kind of sex does not solve the problem. instead, it complicates it since sex is not a pure desire, it is a bestowal from the Almighty Lord to be used to live happily and establish a family with strong ties that is based on love and compassion where every member in the family can satisfy the emotional need of the others and offer support should other family members suffer from the hardships of life. The Said relations can not be achieved by homosexuals. They should cure themselves to be normal people who value life and enjoy all enormous desires given by Almighty God.
There is no recommendation for the man to shave his head when his Aqeeqah is slaughtered.
The Kaffara for deliberate breaking one day of fasting is feeding sixty needy people. Alternatively, it can be fasting two consecutive months. If the fasting begins on the first day of a lunar month, it is sufficient to fast one day from the second month to satisfy the condition of fasting consecutively, and one can separate the fasting of the remaining days as he wishes after that. If fasting started after the beginning of the lunar month, then based on compulsory precaution, 31 consecutive days must be fasted. The remaining fasts do not have to be consecutive.