Is it permissible for a menstruating woman to enter Makkah without the intention of Umrah, then to enter into a state of Ihrām from Taneem after purification to perform Umrah?

If you intend to perform 'Umrah, you must enter into ihram from the miqat, not from Tan'im after purification. If you fear that you will not purify before traveling, then stipulate at the time of ihram: "My place of exit is where I am detained." If you do not purify before leaving Makkah, then exit ihram and depart, and there is nothing upon you.