Yes. Sutta Pitaka: "within me...there arose the knowledge."
Nevi'im, Book of Mormon, New Testament, Modern Prophets: Truth is confirmed by the Holy Ghost in the heart or mind of the individual. In Modern Prophets, D&C 8:2 it states, "Yea, behold, I will tell you in your mind and in your heart, by the Holy Ghost, which shall come upon you and which shall dwell in your heart."
Quran: "[T]he truth is that it is not the eyes that are blind but the hearts that are in the bosoms that are blinded", and "He confers the Spirit by His command on whoever He wills of His worshipers."
View EntriesTorah, Nevi'im, Ketuvim, Book of Mormon, New Testament, Quran, and Modern Prophets: Yes. God does hear and answer prayers. He always answers according to His will. But He also requires that we ask and seek Him in faith. The New Testament states, "Without faith, it is impossible to please God", and admonishes us to "ask in faith."
The Book of Mormon states that God "work[s] not among the children of men save it be according to their faith." God determines what level of faith is necessary for each prayer and each person, but for many prayers He requires faith strong enough to impel us to act, not just a mental assent.