Hi,
Mr.Saikumar is right.
Just because a Co issues a letter does not mean what is stated in the letter is legally correct.
Effective date should be day on which she resigned.
In so far as cut in pay, if the Co is not doing well and wants to reduce pay,they have to take consent of employees in writing. In case, the employee does not want a cut then he has to allowed to quit without notice period.
Regards,
Col.Suresh Rathi