If Jesus’ Authority wasn’t passed from Peter to subsequent Popes, or magisterium, why is it that anyone believes in the Bible?
Because scripture doesn’t depend on the authority of a pope. God’s divine actions in preserving his truths (in scripture and other sources) need no pope, nor an official “magisterium”, though the leaders of the church throughout the first few centuries were certainly involved.
Since non-C’s aren’t ordained in any lineage from Peter, and since non-C’s believe that Jesus’ authority and power stopped with Peter (or that Peter never had any authority or power), where do they derive their power or authority to perform baptisms, perform marriage ceremonies, or to confirm (some do that) in the name of God or through God?
As most protestants don’t hold to the concept of “original sin”, there’s no problem. Also, marriage is a union between two people that need not a priest or other person (though it certainly has become customary in our culture to do so).
Confirmations and dedications, and other things of that sort, are seen as totally symbolic in nature, professing to others a desired path for a young believer (either by parents or by the individual themselves, depending on age).
Mere mortals and lay people don’t have any power or authority to perform these duties do they? Is it just words, or do they believe that God is working through them?
God works through all in different ways. Most of the notably God-used figures in scripture weren’t priests, after all. Do you believe God cannot use “mere mortals and lay people”?
The truth is that no man, even if your concept of the priesthood were valid, has the power to do anything supernatural unless God grants that power. When the apostles and others throughout scripture worked miracles, it was God that either (a) did the miracle working at the request of the man or (b) gave the power to the man to perform the miracle. Only Christ has ever done something of his own accord in this regard, through his divine power.
If they believe that God is working through them, then did God give them the power or authority to perform those functions?
What makes you think that he intended there to be a group of people with one set of “powers” that didn’t apply to the rest of the people?
I didn’t mention the Consecration of the Eucharist, the forgivness of sins in Reconciliation because I don’t think they believe in those sacraments. Am I correct on that?
“The Lord’s Supper”, as it’s frequently called by Protestants, is seen almost always as a symbolic remembrance of Christ’s sacrifice for the salvation of mankind.
Confession is usually seen as something beneficial to the man (when practiced voluntarily), but not as a necessity, particularly in regards to confessing to clergy of some sort. Additionally, such confession is not accompanied by forgiveness on any divine level – only God will forgive, not any man.
Do Non-C’s annoint the sick? If they do, where do they get the power an authority to do that?
Why
don’t they?
When Protestant ministers are ordained, is it through some type of power? Do they receive some kind of power or authority when ordained?
No – it’s a recognition of good spiritual standing (frequently from the congregation which they will serve) and as a symbol of support in their new ministry.