For those who are students or readers of God’s word, can anyone tell me where these beliefs, some of which are largely, (but not all) unique to Roman Catholicism, are found in the Bible?
You dumped so many large topics that I almost passed this up. Really, this should have been separate threads. I am not going to give each its due, as it would make for an obscenely long post. But I'll touch on each.
Did Jesus ever claim to be part of a three headed god?
No. However, there is a point where the gospel refers to baptising in the name of the Father Son and Holy Spirit, and other scriptures that allude to the possible deity of Jesus. IOW it is not clear, and it took the church several centuries to work it out.
Did he ever solicit worship for himself?
Well, he didn't stop Thomas from calling him God and worshiping him, did he.
Was Mary a figure in the Bible to be adored and given undue honor?
Your question is already imbedded with bias when you say "undue" honor. Who are you to say what honor is undue. If she is the mother of the messiah, and if Christians are correct that her "Yes" to God helped bring salvation to the world, I'd say she is due a lot of honor. The question would rather be, why do protestants try to reduce her to nothing? Sounds like knee-jerk anti-Catholicism to me.
Was there a teaching that an immortal soul would depart from the body at death?
Again, it depends on which verses you stress. I think there's a verse that says to be absent with the body is to be present with the Lord.
Is there such a place as Purgatory in the Bible?
Jesus taught about Gehenna. The Jewish concept of Gehenna is a temporary hell in which we are purified for the resurrection. That sure sounds an awful lot like purgatory to me.
Is there a "hell" of eternal fiery torment for the wicked?
Again, Christian scriptures teach the lake of fire.
Is infant baptism a scriptural?
Unless I'm mistaken, the church baptized whole families. It never says infants were excluded.
Should images be used in worship?
Are you going to exclude pictures as well as statues? No cross at the front of the church? No stain glass windows? How far are you going to go with this?
Was the cross a religious symbol for Christians before Catholicism introduced it?
The Church identified itself as Catholic in the first century -- Ignatius used the phrase "Catholic Church" in his writings. The early church traced a cross on their foreheads. There are also crosses in the catacombs.
Were there "priests" officiating in massive cathedrals in original Christianity?
My undertanding is that etymology of the English word Priest comes directly from Presbyter aka the Greek word Presbyteros which means elder. Such Presbyters did exist in the apostolic church, and their descendents via the unbroken chain of laying on of hands do exist today. It's just that this doesn't matter to you the way it matters to some.
Were those who were shepherds in the congregation to wear distinctive garb and headgear and accept titles?
Dinstinctive garb? I have no idea. Titles? Yes absolutely: Presbyters, Bishops, and Deacons (Presbyteros, Episkopos, and Diakonos).
In addition to this, I'd like to mention that the early church also:
* believed in salvific baptism
* believed in real presence in the eucharist (communion)
* accepted the authority of the Presbytery (IOW was not scripture alone)
Again, each of these items is subject for a thread of its own, so I'm not willing to go into detail on any one of them, since this is a kind of gloss over them thread.