What is the ruling on someone who prays and fasts but does not believe in some of the rulings of Sharia? Are his prayers and fasting valid, and can he be called a believer?

Doubting a religious ruling is not considered disbelief (kufr) unless the ruling is known to be an essential part of the religion (maʿlūm min al-dīn bi-al-ḍarūrah), and the doubter has no excuse for their ignorance. For example, doubting the prohibition of adultery or alcohol, or the obligation of prayer, and similar matters that are known to be essential, is considered disbelief. However, doubting something that is not known to be an essential part of the religion does not necessitate disbelief, such as doubting the grandmother's share of one-sixth (in inheritance). What is considered an essential part of the religion varies according to individuals, times, and places. The apostate's acts of worship are of no benefit to them while in a state of apostasy.