No, the disciples were Christ's emissaries. They are not mediators between us and God. There is only one mediator.
The next question is difficult to answer, because the Bible isn't specific on the matter, and the answer is and always has been a bone of contention. I tend to believe what Paul believed for several reasons. But, It's one of those things that we'll find out when we get there.
As for dear Mary, who was just a child when she said yes to God. I asked the girls my youth group if they would have said yes, and they all said they would. Then I told them if they said yes there were men with machine guns ready to mow them down when they left the building, would they still say yes. Because that is what Mary faced. Death by stoning. Then she went to the house of a Pharisee to announce her condition. That took guts. Joseph didn't believe her.
She was 9 months pregnant and bounced her way to Bethlehem on a donkey. And she watched her baby boy suffer and die a horrible death. I don't know how she did it. God sure did pick the right girl for the job.
Is she a mediator between us and God? No. There is only one. Are we told in the Bible to pray to her? No. It is our Father who hears our prayers.
Luke 11: 27-28
As Jesus was saying these things, a woman in the crowd called out, “Blessed is the mother who gave you birth and nursed you.”
He replied, “Blessed rather are those who hear the word of God and obey it