What is the history of Marion Worship and the Rosary beads prayers?? Is there Pagan history?

No one in the Catholic Church "worships" any "Marion".

Catholic prayers are neither mantras nor used to "enter" any kind of "trance".

1) What is the history of Marion Worship

Since you also mentioned the Rosary, I assume that you are referring to the Roman Catholic practice of the veneration of Mary as "worship".
However: Roman Catholics are explicitly taught
- worship God alone
- worship of any statue is forbidden
- worship of Mary or of any of the other saints is forbidden

So: what YOU perceive as worship, the Roman Catholic themselves do NOT perceive as worship. That is why Catholics answering you here tell you, "We don't worship Mary". It's because they do not believe that they are worshiping her.
And...if they do not think they are worshiping her, isn't it true that they are NOT worshiping her? Can you worship someone without realizing it?


2) and the Rosary beads prayers?? Is there Pagan history?

Here is a non-Catholic history of the Rosary.
https://en.wikipedia.org/wiki/History_of_the_rosary
Here is a Catholic history of the Rosary
http://www.theholyrosary.org/rosaryhistory

Although clearly the use of a general type of prayer beads predates Christianity, the specific type/style of prayer beads known by Catholics as "the Rosary" originated within Christianity itself in the 13th century or later.


3) when did Catholicism take it as gospel??

They still have not done so.
I've already addressed the fact that they teach that worship of Mary is forbidden.
The Rosary is strictly an optional belief. A Catholic is not required to pray the Rosary and is not required to believe that any special blessing comes from praying the Rosary. Probably most Catholics have never used a rosary.


4) Some other religions of heathen/pagan ideology has them did Catholicism take them on board as an act of similitude?

Certainly prayer beads predated the Catholic Rosary.
However: it's also true that prayer beads (not the Rosary) were used in Christianity centuries before the Rosary, both inside and outside of Catholicism.
So: one cannot reasonably argue that the Rosary was adopted directly from paganism.
One can argue that using prayer beads as a tool to keep track of prayers was adopted from paganism.


5) WHy are they used is it a mantra to enter a Trance?

That is not the purpose of the Catholic Rosary.
Rather: those Catholics who believe in the Rosary believe that they will gain special blessing by completing the Rosary.
https://en.wikipedia.org/wiki/Fifteen_rosary_promises
It is also used as an aid to meditation.
https://en.wikipedia.org/wiki/Rosary#Devotions_and_spirituality