Why do Catholics pray to Mary?
First I think there is one major distinction to make. Protestants don't understand that there is a difference between prayer and worship. Since Protestants lack the Mass, they cannot understand the difference.
So Jesus is a king in the line of David. In the Davidic kingdom the king's mother was the queen. People would petition the queen to ask the king for favours on their behalf. When Jesus told John, here is your mother he made Mary the mother of all mankind - she is the new Eve as Jesus is the new Adam.
So we petition Mary to pray for us and to help us be like her in loving her son.
Why do archbishops, cardinals, and the pope carry the Lituus?
That is a pretty specific question - and rather biased in presentation. The origin of the Crosier is unknown.
Some writers trace an affinity with the lituus, or rod used by the Roman augurs in their divinations, while others again trace in the crosier an adaptation of the ordinary walking-sticks which were used for support on journeys and in churches before the introduction of seats (Catalani, Pont. Rom., Proleg., xx). At all events, it came at a very early date to be one of the principal insignia of the episcopal office. Just how soon is not easily determined, since in the early passages of the Fathers in which the word occurs it cannot be ascertained whether it is to be taken literally or metaphorically (see 1 Corinthians 4:21) or whether it designates an ecclesiastical ornament at all. In liturgical usage it probably goes back to the fifth century (Kirchenlex., s.v. Hirtenstab). Mention of it is made in a letter of Pope Celestine I (d. 432) to the Bishops of Vienne and Narbonne. Staffs have indeed been found in the catacombs that date from the fourth century but their ceremonial character has not been established. The first unequivocal reference to the crosier as a liturgical instrument occurs in the twenty-seventh canon of the Council of Toledo (633). At present it is employed by bishops whenever they perform solemn pontifical functions, by right in their own dioceses and by privilege outside, and by inferior prelates whenever they are privileged to exercise pontifical functions.
You might as well ask why did Moses carry the Lituus. Popes don't currently use the Crosier.
Why is Easter celebrated on Sunday when Jesus is said to have died on Friday, and resurrected after three days and three nights?
It has to do with how the Jews counted time. Any part of the day counted as the whole "day & night."
Why is there a statue of the roman god Jupiter in the Vatican?
There isn't. This ancient statue of St. Peter, portrayed as he gives a blessing and preaches, while holding the keys to the kingdom of heaven is thought by some scholars to have been a work of Arnolfo di Cambio (1245-1302), others believe that it is a V century casting. Either way not Jupiter/Zeus/Whomever.
Why do Catholics celebrate Christmas at the winter solstice knowing full well that according to scripture, farmers were out in the field when the three wise men visited the manger?
Because it is Biblical.
We know that Elizabeth is in her 6th month of pregnancy when Jesus is conceived.
And behold, yourkinswoman Elizabeth in her old agehas also conceived a son; and this isthe sixth month with her who wascalled barren. For with God nothingwill be impossible.
So if we can establish when John the Baptist was born we can establish when Jesus was born.
Saint Luke reports that Zacharias served inthe “course of Abias” (Lk 1:5) which Scripturerecords as the eighth course among the twenty four priestly courses (Neh 12:17). Each shift ofpriests served one week in the temple for twotimes each year. The course of Abias servedduring the eighth week and the thirty-secondweek in the annual cycle. However, when didthe cycle of courses begin?
In our calendar, the Day ofAtonement would land anywhere fromSeptember 22 to October 8.
Zacharias and Elizabeth conceived John theBaptist immediately after Zacharias served his course. (See Luke 1:5-24) This entails that Saint John the Baptistwould have been conceived somewhere aroundthe end of September, placing John’s birth at theend of June.
Add six months to the end of June and you get the end of December for the birth of Jesus - hence December 25. For a fuller description:
Why does the Roman Catholic Church have a persistent issue--one may argue institutionalized--with their priests and pederasty?
One doesn't become a saint as soon as they put on a collar. There are many things I could discuss like the infiltration of the Catholic Church by communists in the 30, and their letting gays into the priesthood. However, this is the deepest shame to the Church that any priest should do something like this. The number of abusing priests was roughly equal to that number in the general populace.
It is not a problem only for Catholic clergy:
It was meant to be symbolic of the crushing of Satan's head as noted in Genesis. I personally think the whole thing is ugly. Many poor things have been done artistically since Vatican II. Bad art is bad art, yet it doesn't invalidate any teachings. Artistic interpretation is not protected by the Holy Spirit.