Muslims are not the only ones who believe that Jesus (pbuh) is mortal and not a god. The Jews also believe this, in addition to the very first groups of Christianity such as the Ebonites, the Cerinthians, the Basilidians, the Capocratians, and the Hypisistarians. The Arians, Paulicians and Goths also accepted Jesus (pbuh) as a prophet of God. Even in the modern age there are churches in Asia, in Africa, the Unitarian church, the Jehovah's Witnesses, and even the majority of today's Anglican Bishops do not worship Jesus (pbuh) as God.
Please clarify your question. Which synagogue are you speaking about?
Jesus teaching in the synagogue was significant because it demonstrated his authority and knowledge of scripture, which impressed the people and challenged the religious leaders. It also marked the beginning of his public ministry and the fulfillment of his role as the promised Messiah.
There is no evidence in Scripture or any outside sources that Jesus visited or spent time at the Qumran community.
As this question appears to be referring to the Wise Men (Magi) in Matthew 2, then the Scripture is silent on their names and number of them visiting the child Jesus in the house.
According to Luke 4:18, 19, the passage Jesus read was Isaiah 61:1, 2. The crowd took exception to what Jesus said in Luke 4:21 - "Today this Scripture is fulfilled in your hearing."
In the time of Jesus in Israel the religious houses were called synagogues, and yes Jesus preached in these. In Luke 4:16-30 is the story of Jesus going to the town he was raised in and preaching in that synagogue.
The Scripture is silent on the number and names of the Wise Men (Magi) visiting the child Jesus in the House. It could have been 1 or a dozen or more.
The account of Jesus reading in the synagogue is significant in showing his authority and fulfillment of prophecy. It demonstrates his role as a teacher and his mission to bring the message of salvation to all people. This event also highlights the importance of scripture in his teachings and the continuity between the Old Testament and his ministry.
Judaism has many formal clothing requirements (the tallith, the yarmulkah ...), so it would be fair to say that Jesus wore school-uniform both when he was at study and also when he attended the synagogue. (Though there no evidence of a synagogue in Nazareth has ever been discovered).
As an observant Jew of his time of course he did, however according to the Gospels by age 12 he was astounding the educated Rabbis in the Synagogue with his knowledge of the scripture. No authoritative source addresses anything about his youth beyond his visit to Jerusalem and teaching the learned people in the temple when he was around 12, We may assume that since all boys of his time were expected to spend some time learning in the synagogue that Jesus did as well, but that is only an assumption.
At jesus time scripture were read from schrolls.
The temple was the place for the offering of sacrifices. Maybe you are thinking of the synagogue. Jesus was not debating, he was sitting listening to the teachers and asking them questions. Where does the Scripture say this was not allowed?