Every single objection you have made can be answered. Please understand that we have on our board some of the most educated Greek scholars you will find, that have been studying the Bible in its original languages for many years. I know some Greek and am able to explain those answers to you, but we can have it verified by others if you wish.
Doctrine is not your only problem, however.
It is history. You are beating around the bush. If you cannot demonstrate that Peter was ever in Rome, or the bishop or Rome, or the bishop of the church at Rome for any extended period of time then your whole theory and all the perpetuated lies of the RCC falls apart. And that is the truth.
It is a simple thing to do. I can prove that he wasn't in Rome for any length of time (if at all) just by using scripture. Other sources gives credence to the view that he never made it there at all.
The mistake lakeside makes is he thinks I am coming at this from a Protestant perspective. When I started investigating all this, and all religions, I didn't have a perspective. I was an agnostic and near-atheist. I wanted to know the truth, whether that lay in Christianity or another religion, or no religion. When I decided that Christianity was true, I then narrowed my search to what doctrines, practices, and church(es) was/were true. I discovered that the RCC claims were false; they could not be substantiated from scripture, the Fathers, the early churches, from early church history. The RCC is an organization which is an amalgamation of the Roman Empire, pagan religion, and a few Christian teachings. It has been the worst persecutor in the history of Christianity. See, this is the way Satan works. If anything were completely false, it would clearly be recognized as such and could gain no power or adherents. But take a little truth and mix it with a lot of falsehood, money, greed, and earthly power, and you have the perfect false "church". There is no way -- I repeat, NO WAY -- that the church which Jesus founded could have spilled all the blood that the RCC has spilled over the centuries. That alone reveals the RCC as an impostor.