“Was Mary (the mother of Jesus) a Christian? Is there any clear statement in the New Testament Scriptures that she was, in fact, a member of the church that Jesus built?”
No, there is no expressed statement in the Bible that Mary became a Christian. However, the thrust of everything we read about Mary indicates that she would have, and probably did. Seemingly, Mary believed in the divinity of Jesus from the time the angel announced to her, “You will conceive and give birth to a son, and you are to call him Jesus. He will be great and will be called the Son of the Most High” (Luke 1:31 – 32, New International Version). Why wouldn’t she believe Him to be the Son of God, when the angel of God had clearly told her that He was?
When Jesus astounded others (at the age of 12), with His wisdom and knowledge, it is simply stated, “…his mother treasured all these things in her heart” (Luke 2:51). Mary was involved at the first miracle Jesus did, and Scripture indicates that she knew He had the power to do it (John 2:1-5).
Mary was there at the cross when Jesus died, along with other women who believed. And she was numbered with the 120 disciples who prayed together in Jerusalem after the ascension of Jesus and before the church began (Acts 1:14,15). It is implied (in Acts chapters 1 and 2), that these 120 were disciples and were either “set in” (I Corinthians 12:18) or were “added to the church” (Acts 2:41, 47). If that is true (and I believe it is), then Mary (as part of the 120) was a Christian, a member of the church.
“What happened to Joseph (the husband of Mary)? We don’t find anything about him after the birth of Jesus.”
When Jesus was a baby, the angel of God told Joseph, “Get up! Take the Child and His mother and flee to Egypt…” (Matthew 2:13, New American Standard Bible). When Jesus was presented at the temple, Joseph was there (Luke 2:22). Later in the same chapter, we read of the event where Jesus was left in Jerusalem by “His parents” (verse 41) at the age of 12. Joseph was around at that time. But that is the last time we read of Joseph in the Scriptures.
Many supposed that Joseph was much older that Mary, and that he died before Jesus began His ministry at the age of 30 (Luke 3:23). In any case, we read no more about Joseph in the Scriptures after Jesus was 12. And it seems strange, if he were still alive during Jesus’ ministry, that Joseph was never mentioned. The mother, brothers and sisters of Jesus are mentioned several times, but not Joseph. Indications are that Joseph was dead by that time, or he would have been named with some of the events in the life of Jesus. But that is still only an assumption. We just don’t know what happened to Joseph.