Neither of those questions makes Mary a Christian’s mother.
You have a mother. It isn’t Mary.
If you are a believer, she is your sister.
The questions don’t; the answers do. We’re making progress, though: at least you’ve admitted Mary into the family! “Sister” is a proper title for other Christian women who are our relatives in the faith, yes. But we also see titles of spiritual genealogical descent used in the NT—for instance, Paul calls his own disciples at Corinth “dear children” and says he is their “father” (1 Corinthians 4:14), and John uses the same language when writing to his disciples (1 John 1:12f). Jesus calls Mary John’s “mother”, not his “sister”—she is not just any female believer, she is the very first female believer, the first female to hear the Gospel from the angel Gabriel (Luke 1:28). She was with Jesus before any other human being, and she is the only person who stayed with him his entire life, from birth right to the Cross. “Mother” conveys this special relationship better than “sister”—especially since she was also Jesus’ literal mother.