The keys to the kingdom of heaven are the gospel of our Lord and Saviour Jesus Christ. Peter was given them to preach to the Jews. The rest of the apostles and disciples, including us today, have the keys. They aren't locked up in the Vatican.
Not likely, because the "keys" of the Gospel were given to all of the Apostles, while Mt 16 has Christ saying to Peter "I will give to you (singular) the keys of the kingdom". He further confirms this in Luke 22:32 when he says "I have prayed for you (singular) that your faith may not fail, and when you (singular) have converted, strengthen your brethren". And then there's John 21:15-19 ...