The Greek is "petra", feminine, means "rock". "Petros" is not used anywhere in the patristic period; "lithos" is used for "pebble". The most natural reading is that Jesus simply makes a masculine proper noun from feminine common noun, since Simon is a man. The conversation most likely took place in Aramaic anyway.
The idea of Peter being the "head of the church" can't be supported anywhere else.
Peter is also given the keys to the Kingdom, asked to feed the sheep and is told that Christ will pray for him so that he converts his brethren. These are all things that apply individually to St. Peter. He also sets in motion the first major reform of the Chruch at the Jerusalem council, -- if it were not for Peter, you would not be able to enjoy lobster. Head of the Church he is not called indeed, because Christ is.
Compare Matthew 16 with 18 regarding binding and you'll see that the keys are not unique to Peter, all Christians have them.