If the man have issued the first two divorces and the woman issued the last one. Would that count as the final divorce or must it be 3 divorces from the man?
Short answer: Yes.
Note that a "legal" separation of spouses can be achieved in three ways:
talaq الطلاق this is basically what people first think of if we speak about divorce as it is an uttered divorce and which I will explain in more details as it seems to be what you are asking about: Note that nowhere in the qur'an Allah speaks of divorced men, but you may read instead:
- Divorced women remain in waiting for three periods, and ... (2:228)
- And if he has divorced her [for the third time], then she is not lawful to him afterward until [after] she marries a husband other than him. ... (2:230)
- And when you divorce women and they have [nearly] fulfilled their term, either retain them according to acceptable terms or release them according to acceptable terms, and do not keep them, intending harm, to transgress [against them]. ... (2:231 see also (2:232) which starts with the same sentence.
- There is no blame upon you if you divorce women you have not touched nor specified for them an obligation. ... (2:236)
- And for divorced women is a provision according to what is acceptable - a duty upon the righteous. (2:241)
- O Prophet, when you [Muslims] divorce women, divorce them for [the commencement of] their waiting period and keep count of the waiting period, and fear Allah , your Lord. ... (65:1)
all these verses show that divorce or talaq is in the hand of the husband and only he can utter it. And after two talaqs the third is crucial as there's no option of reconciliation as Allah says:
Divorce is twice. Then, either keep [her] in an acceptable manner or release [her] with good treatment. ... (2:229)
khul'a الخلع is a legal way by which a wife can buy herself free from an unhappy marriage for this she must apply for a familly court and it is recommended that she shouldn't pay more than the mahr she has received from her husband.
- faskh الفسخ is a legal way by which two people can be separated and the marriage can be declared as invalid (needs a court too).