From Wikipedia:
"Irenaeus (Greek: Ειρηναίος), (c. 130–202) was bishop of Lugdunum in Gaul, which is now Lyon, France. His writings were formative in the early development of Christian theology, and he is recognized as a saint by both the Eastern Orthodox Church and the Catholic Church; both consider him a Father of the Church. He was a notable early Christian apologist. He was also a disciple of Polycarp, who himself was a disciple of John the Evangelist."
No, he didn't follow the Roman State (pagan) religion.
Heresy assumes a common agreed upon orthodoxy taught by the bishops of the church. They had the authority in the local churches. He wouldn't have had to convince believers who were in the church. His authority was that he taught what had been pasdsed down from the apostles ( John --> Polycarp --> Irenaeus) but htat was true of all of the bishops. It is the role of the bishop to protecct the truth.
And wherever did you get the silly idea that Matthew was written in the 4th century? I know of no scholar at all who would agree with that!
You "supositions" are just uninformed guesses.
Irenaeus refered to Matthew written in Hebrew. This may have been in Aramaic, which is written with Hebrew letters.
http://www.godglorified.com/matthew_2819.htm
Reference above notes modifications to Matthew in the 4th Century.
No doubt there were earlier texts which informed the 4th Century author. All of Mark can be found in Matthew.