When Jesus said no one comes through the Father through Him, He wasn’t speaking of prayer. He was speaking of literally coming to the Father [Joh 14:6]
He was speaking of the same coming to the Father of which He spoke to Nicodemus, when He said one must be born again to enter God’s kingdom, and of the true worshippers who worship God in spirit and truth
This doesn’t mean that praying in Jesus’ name is wrong. It’s right to pray in Jesus’ name—only that’s not what the verse is teaching.
Jesus said to the twelve, “believe me that I am in the Father” [Joh 14:11]. He was speaking directly to the disciples with Him at that time. Then in the following verses, He says “whoever believes in me will do the works I have been doing”
[Joh 14:12]. Those who believe in Him—those who will do the works He does and greater—are those to whom He spoke in the previous verse—not the entire Church.
The Apostles will do greater works because Jesus goes to the Father [Joh 14:13].
This happened because Jesus will ascend to the Father’s right hand.
Interestingly, Jesus—not exactly His Apostles—is He who will do the greater works. This is seen when Jesus said that when they ask in His name, He—Jesus—will do what they ask [Joh 14:13].
This doesn’t only apply to the twelve, but to those Jesus send. Neither Paul not Barnabas were of the twelve, but were also sent by God, and great signs followed them.
Apostles are supposed to have signs following them [2Co 12:12].
Note that it doesn’t say that these signs will follow all Christians, but Apostles.
Apostles are also supposed to have revelation of the truth of God’s word [Eph 3:5].
The Gospels and Acts are written not just to talk of Jesus, but of the establishment of the Church, and of the Apostles. This is seen in the emphasis on “the Disciples and Peter” [Mar 16:7].
Jesus sent the Apostles to go to the world and preach. He told them that those who believe will be saved and those who don’t, would be condemned. He proceeds to say that signs shall “follow/accompany”, those who
believe, but the people signs “follow” are those who are sent [Mar 16:15-17].
“and they went forth preached and confirming the words with signs following” [Mar 16:20].
This confirms that the signs follow those who are sent to preach, not just those who believe.
For the entire Church however, after the first resurrection, the signs will follow all who believe.