So, this user on Reddit has been posting some amazing infographics explaining Catholic theology, especially the connection between Old & New Testaments.

Let me present 3 wonderful infographics from "Defense of Sanity." https://www.reddit.com/user/Defense-of-Sanity/

The Eucharist is seen in the commands to eat given in the OT: Melchizedek tells Abraham, the Passover celebration, the Mana in the Desert & Ezekiel's Scroll.
The Eucharist is also parallel to the fall but reversing it.

The Gospel of Luke links Mary to the Ark of the Covenant through overshadowing, dancing in her presence, etc.
Jesus represents the three items in the old ark: bread, word, and priest.
This shows us that Mary is pure.

Finally, an infographic on the Pope.
He is the Rock in Matthew 16, he is given the keys like Isaiah was, he has authority, and has a line of succession. Jesus designed his Church to have a chief steward: The Pope.

Purgatory is a purification to enter Heaven, not some intermediate place.
Sin has 2 effects and confession/absolution only cleanses us of the more serious effect leaving purgatory to clean the less dramatic effect.
We can find references to Purgatory in what Paul & Jesus said

The 1st Christians believed:
The Eucharist was Literally Jesus
You confess to a priest
You baptize infants
Purgatory exists
Mary was sinless