Does God only hear and answer the prayers of worthy members of the Latter-day Saint church?
We need to realize that God is the Father of all mankind. He is interested in the prayers of all those who faithfully pray to him. It is through prayers of the faithful that all knowledge is given us. We are told when we have read the Book of Mormon to ask God if it is not true. This is found in Moroni 10:4-5.
4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.
This promise is given to all, not just Mormons.
There are many testimonies of people who are not members of the Mormon Church concerning the answers to their prayers.