Is there a gospel of Peter? Is there a place online where I can read it?

No.

this is another error that people make because they don't have the brains to actually read the Bible and to go back to the original language Jesus Christ spoke to Peter the word Peter means Little Rock Jesus Christ said to Peter your name is Peter which means Little Rock but upon this rock pointing at himself I will build my church.

There is a Gospel of Peter, but it was rejected as not authentic. Better to stick with the letters he wrote in the Bible.

BTW, Jesus didn't say Peter was the founder of the church.

No, there is no Gospel of Peter. If there is such a work, it is probably Gnostic in origin, and was created by someone else long after Peter's death, like most of the apocrypha. I wouldn't waste my time on it. It's sure to lead you into deception, as all the apocrypha do. And Jesus did never say that Peter was the founder of the church. In point of fact, there was already a church body of believers in Rome when Paul went there, and Peter followed him to there many years later, and tried to shore up the church that was there. So he didn't found it, and neither did Paul. Also, I think you are referencing the passage where Jesus calls Peter a pebble, but states that it is the Rock upon which Peter has based his belief, that Jesus was the Christ, is the Rock upon which He will build His church --- and then a few passages later, Jesus calls Peter Satan and tells him to get behind Him (to get out of Jesus' way). Funny when people take this passage completely out of context, and then totally gloss over the later passage.

You may search at Sacred Texts.

Yes there is a gospel of Peter. It is a heretical gospel not included in the bible. You might be able to find it at a bookstore. I have a book called "The Banned Books of the Bible". And you could most likely find it online.

Who was the rock that Jesus indicated at Matthew 16:18, Peter or Jesus?

The context shows that the point of the discussion was the identification of Jesus as “the Christ, the Son of the living God,” as Peter himself confessed. Matthew 16:16

Logically, therefore, Jesus himself would be that solid rock foundation of the church, not Peter, who would later deny Christ three times.

How do we know that Christ is the foundation stone? By Peter’s own testimony, when he wrote “And you have been built up upon the foundation of the apostles and prophets, while Christ Jesus himself is the foundation cornerstone.”

There is no evidence in Scripture or history that Peter was regarded as having primacy among his peers.

He makes no mention of it in his own letters, and the other three Gospels including Mark’s do not even mention Jesus’ statement to Peter.

There is not even any absolute proof that Peter was ever in Rome. 1 Peter 5:13

When Paul visited Jerusalem, “James and Cephas and John, the ones who seemed to be pillars,” gave him support.

So at that time Peter was one of at least three pillars in the congregation. He was not a “pope,” nor was he known as such or as a primate “bishop” in Jerusalem.

At any rate, the assertion that the papacy was founded by Jesus is simply not supported in the Bible. According to the Encyclopedia of Religion, even modern Catholic scholars concede that “there is no direct biblical proof that Jesus established the papacy as a permanent office within the church.”

The inspired Scriptures, including the two letters written by Peter, make no mention of his going to Rome. Paul speaks of being in Rome but never refers to Peter’s being there.

No, and when did he say that?

That's why we like to call modern Christianity, Paulianity.

Jesus never said Peter was the founder of the church.