1) you dont have to pay any tax on apartment which is in your wife name
2) gift by father in favour of daughter would be exempt from gift tax
3) As per the Income Tax Act, 1961 if the value of gifts received is more than Rs. 50,000 a year, then such amount is taxed as income in the hands of the receiver. These gifts may be in any form – cash, jewellery, movable and immovable property, shares etc.
However, this rule is not applicable if your relatives present the gifts. , the income tax rules specify relatives from whom tax free gifts can be received. These are:
Parents
Spouse
Your and your spouse’s brothers and sisters
Brothers and sisters of your parents
Your lineal descendants (including spouses)
Lineal descendants (including spouses) of your spouse
4)you can purchase flat in joint names . later father can gift his share in flat to daughter . stamp duty on gift from father to daughter attracts nominal stamp duty of Rs 200 in Maharashtra . registration charges are also nominal Rs 200