Your understanding of the Catholic belief is very close to what I was taught by Catholic priests. Prayer to Mary and the saints is based on the story of Jesus' first recorded miracle. Jesus was not going to perform a miracle at the wedding that day and even argued against doing so. When his mother requested he perform a miracle, he told her his time had not yet come. Mary pleaded with him and successfully convinced him to perform a miracle that it is clear he otherwise would not have performed. Thus, Catholics teach that Mary, as the mother of God, and the saints, who are considered his friends, are able to plead your case to God who may be moved to perform a miracle that he otherwise might not have performed. Thus, it's not so much that any authority was delegated to them, but rather that they can plead on your behalf.

The dominant protestant belief is that you may only pray to God. Prayer to Jesus is often considered acceptable because his role in the trinity makes prayer to Jesus synonymous with prayer to God.

I'm not sure why you bring gender into the discussion, it isn't anything I addressed and seems to have nothing to do with the discussion at hand.