(1-3) If you give written talaq bayin to your wife and do not condition the written talaq with something then talaq shall occur on your wife though you tear off the talaqnama later and throw it and do not send to your wife. If the talaqnama mentions about one talaq bayin then you may keep your wife with you after new nikah within iddah period or after iddah. After new nikah, the husband shall have only the right of two talaqs and if any time in future he gives two more talaqs, then all the three talaqs shall take place and the wife shall become mughallaza bayina and haram.
(2) According to the Shari’ah only husband has the right to pronounce talaq not the wife. If the wife sends talaqnama then it will not be taken into consideration as per the Shari’ah.
قال عليه السلام: انما الطلاق لمن أخذ بالساق . رواه ابن ماجه.
Allah knows Best!
Darul Uloom Deoband