Is it Halal for a Muslim woman to cut her hair short exactly like a man?Is it Halal for a Muslim man to let his hair grow long like a woman?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Concerning women's hair please refer to Fatwa: 81850 .
Growing long hair is permissible for men as long as they are not imitating Kuffars, dissolute persons or imitating women. There is no certain limit legislated in Shariah for lengthening one's hair. However it is recommended to follow the Prophet Muhammad (Peace and blessing be upon him) in this case too.
Imam Ibn al-Qayyim said: 'The hair of the Prophet did not reach the shoulders but it exceeded the ear-lobes. Sometimes when it exceeded this length he would interweave it into four braids'.
Please read the Fatwa: 82852.
Allah knows best.