Your reference to Peter is true of the Roman Catholics, but not the rest of us that this forum covers. The rest of us agree with the Fathers that the primacy of Rome was not due to some special inheritance from Peter (in any case there are two other Patriarchates with equally good and prior claims to Petrine succession) but rather due to the political and cultural importance of the city of Rome and the honour aforded her by the martyrdoms of both Peter and Paul in the city. In any case, Peter was never Pope of Rome (even according to Church Fathers) and only ordained their third Pope, the first two being ordained by Paul.
The truly Catholic position, the one that everyone in the Church would have recognised as such before we were separated, is that valid priesthood is passed on by Apostolic succession, not Petrine succession (though Peter is viewed as the type of the Apostles). Until just now I'd always thought that Rome still believed that. Whilst I knew that they claim universal jurisdiction for the Pope of Rome, I had no idea that they claimed all priestly authority comes through him. I hope this isn't true.
As for the claim that the Pope ordained all bishops, that's pure nonsense. For a start the canons are clear that all bishops must be ordained by three others (not one) and secondly, the Church was historically divided into five patriarchates and it was uncanonical for any Patriarch (including the Pope) to ordain clergy in across those boundaries.
James