Where does the Bible say the early churches treated Peter in a papal fashion?
I cite the example of Peter settling the circumcision debate in Acts 15.
Where does the Bible say that one man is the head of all churches?
see my answer to the first question.
Where does Bible say God established a special priesthood for the churches that is separate from the priesthood of the believers? Where does the Bible describe the office of such priests in the early churches? Where does the Bible say that New Testament priests are ordained after the order of Melchizedek?
These questions can be answered together as they refer to the sacrament of Holy Orders. The Eucharist is the reason why priests are ordained so they can perpetuate the Eucharistic sacrifice in the Church.
“For every high priest chosen from among men is appointed to act on behalf of men in relation to God, to offer gifts and sacrifices for sins.”
“He can deal gently with the ignorant and wayward, since he himself is beset with weakness.”
“Because of this he is bound to offer sacrifice for his own sins as well as for those of the people.” (Heb 5:1-3)
“being designated by God a high priest after the order of Melchizedek. “(Heb 5:10)
I can't post my whole response on one reply so I'll have to do several.
Where does the Bible say the apostles passed on their authority through a succession?
I will cite the example of Matthias being elected to replace Judas in Acts 1.
Where does the Bible give standards for apostolic succession? There are standards for pastors and deacons, but where are the standards for an ongoing apostleship?
Apostolic succession is based on the mission Christ gave the Apostles. "As the Father hath sent Me, I also send you: (John, 20:21). Since this is a divine mission it must always continue the same, and is transmitted with its Divine character until the end of time. We call this unbroken lawful succession Apostolicity. We have the example of Paul, in his Epistle to the Romans insisting upon the necessity of this Divinely established mission. "How shall they preach unless they be sent?" (10:15). Paul also instructs his disciples Timothy and Titus, of their obligation of preserving Apostolic doctrine, and of ordaining other disciples to continue the work entrusted to the Apostles. "Hold the form of sound words, which thou hast heard from me in faith and in the love which is in Christ Jesus" (2 Tim 1:13). "And the things which thou hast heard from me by many witnesses, the same commend to faithful men, who shall be fit to teach others also" (2 Tim 2:2)
Where does the Bible describe nuns in the early churches?
They are not referenced specifically in the bible however Paul speaks of widows, who were called to certain kinds of church work (1 Tim 5:9, and of virgins (1 Cor 7 ), whom he praises for their continence and their devotion to the things of the Lord.
Where in the Bible do we find anyone praying to Mary or to any other person other than God?
You are referring to intercessory prayer and our teaching of the communion of the saints. This has been discussed numerous times however, I will give a few scripture references where examples of this can be found Col 1:9; 2 Thes 1:11; 2 Thes 3:1; Jas 5:16)
Where does the Bible call Mary the Mother of God?
We base this teaching on the unity of God, the eternity of the Word and the Incarnation. So if Scripture reveals that Mary is the Mother of the Word-made-Flesh, and the Word-made-flesh is God, then Mary is the Mother of God (the Word), not from eternity but beginning in time and for eternity. To say only that Mary is the Mother of Jesus or only the Mother of Christ, is to deny the unity of Christ's Divine and Human Natures.
"blessed art thou among women and blessed is the fruit of thy womb, how is it that the Mother of the Lord comes to me" (Lk 1:42-43).
Where does the Bible say that Mary is the Queen of Heaven?
Mary’s Queenship is first based on her maternal relationship with Jesus. Since Jesus is certainly the Messianic King, it follows that Mary’s role is that of the Queen Mother of the Messianic King. We also see scriptural evidence of this in Revelation 12:1 describing a “woman clothed with the sun, with the moon under her feet, and on her head a crown of twelve stars”.
Where in the Bible do we find the teaching that Mary is sinless?
This teaching is based on Luke 1:28 where Mary is described as full of grace. We believe that being in such state is entirely consistent with a status of sinlessness. We also believe that God can make a person sinless if He so desires. If he originally made Adam and Eve that way, why not the mother of God our Savior?
Where in the Bible do we find the baptism of an infant who is too young to believe in Christ?
Two points here. We know that baptism replaced circumcision as the method of entering into God’s covenant family (Col. 2:11-12). We also have the examples in the book of Acts of whole households and families being baptized.
Where does the Bible teach us that the church can identify dead people as saints and can then pray to them? Where does the Bible teach that a dead person can intercede for the living?
see my previous answer regarding communion the saints and intercessory prayer.
Where does the Bible teach about purgatory?
The explicit scriptural reference is 2 Mac. 12:42-46. Paul also tells us that at the judgment each man's work will be tried. This trial happens after death. And what happens if a man's work fails the test? "He will suffer loss, though he himself will be saved, but only as through fire" (1 Cor 3:15).
Where does the Bible teach that churches should use the bones of dead men in any type of religious manner?
This question refers to the Catholic practice of relics. We do have examples of this in the NT. A woman was cured of a hemorrhage by touching the hem of Christ's cloak (Matt. 9:20-22). The sick were healed when Peter's shadow passed over them (Acts 5:15-16). "And God did extraordinary miracles by the hands of Paul, so that handkerchiefs or aprons were carried away from his body to the sick, and diseases left them and the evil spirits came out of them" (Acts 19:11-12).
Where in the Bible do we find Peter assuming and exercising the role of a Catholic pope?
This is based on Matt 16:18. In the interest of thread space I will provide one example. Jesus says, "I am the good shepherd" (Jn.10:14) and to Peter "Feed my sheep" (Jn.21:15-17) which means "teach my Church." So we view Peter and his successors as the chief shepherd of His church. Christ is the invisible head of the Church, the Peter and his successors are the visible head.