I want to become an Aalim (scholar). Is this possible for me as a lady and can I do this in Saudi? If yes, please tell me where and how?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
As for studying in K.S.A you may contact the educational authorities in that country; surely they will help you.
You may apply at the American Open University. The course of this university is generally good.

Allah knows best.