This question is very biased and very misinformed. But I'll try to answer the objections or assertions as they come up:
"what is seen as the worship of Mary"
First of all, worship of a creature (and therefore Mary; saints) is the grave sin of idolatry—giving to a creature what is due to God alone. This doesn't happen in the Catholic Church, because it teaches that such, like all mortal sin, will damn you to Hell, if unrepented of (that is, making all abuses of this Catholic teaching, by definition, not catholic).
The outward appearance of worship of God, and the veneration one might afford a King, might look the same. Whereas the difference lies in the intention of the heart, not the appearance (for example, you can worship by simply thinking something within yourself).
A Scriptural example would be:
1 Chronicles 29:20 And David commanded all the assembly: Bless ye the Lord our God. And all the assembly blessed the Lord the God of their fathers: and they bowed themselves and worshipped God, and then the king.
The traditional sense of 'worship' (even in Old English) encompasses both this prostration or profound respect for authority, priests, or royalty, as well as God. They intended to bow down and show respect to the King, and to God, but clearly they were worshiping in one sense to God, and showing respect in another to the King—both by the same outward act.
Ruth 2:10 She fell on her face and worshipping upon the ground, said to him: Whence cometh this to me, that I should find grace before thy eyes, and that thou shouldst vouchsafe to take notice of me a woman of another country?
Outwardly, pagans might accuse the Jews of 'worshiping' the King, or Ruth of 'worshiping' in the divine sense, and not an earthly, kingly sense, Boaz. Just like Catholics are accused of, despite their own teaching, their own faith, and their own testimony to the contrary. Outwardly, whether you are bowing to show respect, reverence, or intend to worship God, is absolutely indistinguishable. Therefore, you'd need to claim to be able to see in the heart of Catholics in order ot say that secretly, despite literally everything that could possibly militate against the idea, offering worship to a saint.
cf. Romans 13:1-7
"you may also add the statues that were remade from pagan"
You mean you may assert that. That has nothing to do with whether it happens to be the case or not.
Most likely, a statue of Mary, is, as both the sculptor and theone who asked it to be sculpted says... *drum roll* ... Mary! And not some pagan this or that.
"The critique is large and it often comes from the rest of the Body of Christ (the church)"
Actually, it's a novelty, and the Church never taught anything like what anti-Catholics teach—and without exception, only as they break off from the Church to start their own sect.
"I will confront the question from the view of Sun god worship"
Which has nothing to do with the Catholic Faith.
"Common knowledge that change came with Constantine (not a controversial view of History)"
Which change? And what documentation from the period substantiates it?
"Suddenly "Christian Holy days" match with pagan dates"
The Catholic Church does not, and could not, hold to the 'copyrighted day of the year by pagans' idea. God owns the year, not pagans. If pagans do something other than what we celebrate onthe same day, or used to, literally, who cares? A Christian holy day is infinitely better than an orgy-fest or whatever the pagans were doing. How could anyone hold the contrary?
"The structure of the leadership in connection to the story of Nimrod"
Why jump from the leadership outlined in the Bible and extremely early Church, to something outside the Church, which had no influence whatsoever on the structure of the Church. The History Channel approach to history doesn't work. If you decide the Catholic Church is pagan you will find something 'pagan' no matter what.
"You see the round wafers in the sacrament and in the monstrance symbolize the sun (the sun was erected above the altars in the worship of Baal)"
Why isn't it a parallel to the round wafers of manna of which the Eucharist is the New Covenant fulfillment, but instead something pagan, yet again? Why are the rays not a shining forth of glory, (Mt 17:2) and instead 'the sun'—and why is the sun taken to be a god, and not a glorious creation of God symbolic of the glory, righteousness and sovereignty of Christ? (Mal 4:2) Did you know He is called the sun of righteousness in the Bible? That like the sun, He clothes His Church in righteousness? (Rev 12:1)
Why do you keep apply in the pagan meanning to symbols used by Christians in purely Christian contexts?
"The wine turns into blood (drinking blood) not just a symbol"
Find me a Christian who ever said that the Eucharist is just a symbol in the Church until hundreds of years later?
Christ, St. Paul, and the disciples of the Apostles all teach the Eucharist is the body and blood of Christ.
Jesus said the bread He gives for the life of the world is His flesh. And that the bread and the wine respectively not symbolized but "[are]" His flesh and blood.
If you want to introduce the novelty of a purely symbolic interpretation, you do so at the expense of claiming to be Christian, and believing in "the Faith once for all delivered to the saints" (Jude 1:3).
"The columns of St Peter's Basilica in Rome have a sun-like image, and a wall has a golden sunburst image just as in the Babylonian temple"
In one, it is a decoration (are God's days of the year kept for pagans only, just like the sun?). In the other, they explicitly worshiped the sun. This isn't difficult stuff.
The Catholic Church reacts to accusations such as these the same way it reacts to 'there were other sons of God before Jesus' claims. By dismissing them as irrelevant to the deeply-rooted-in-Judaism religion that is Christianity, and demanding some sort of proof that the accusers aren't just making connections which never formed the similarities (e.g. Jesus being the Son of God, and other pagans claiming there were sons of God beforehand).