What is religion of the Prophet Mohammad (PBUH) before become messenger of Allah? He is acting according of christian shriah or other Abrahamic religion?
Abrahamic religion was prevalent in Arabia as no other prophet came to Arabia after Prophet Abrahim (PBUH). Arab used to associate themselves with Prophet Abrahim (PBUH), so I think Prophet Muhammad (PBUH) was also following Prophet Abrahim'S (PBUH) religion.
There are indications in different hadith that Holy Prophet Muhammad (PBUH) followed true Abrahamic religion when performing Haj (before becoming a prophet) and did not followed the deviations that the tribe of Quresh (to which Prophet Muhammad (PBUH) belonged)
I searched somewhat, but to be honest I assume the response of your question is relatively long, So I reckon it is not feasible to reply to this question completely. anyhow I found two sites below (reference) which have illustrated it as a detailed response. Look at them please. (Note: unfortunately these are two Farsi sites, hopefully you could read Farsi)
but if I want to mention it briefly, I can classify them in four main classes:
the messenger of Allah (pbuh) was not follower of any religion
He was the follower of Christianity
He was the follower of the religion of Ibrahim (s)
He was the follower of his religion from first (Islam)
To see the detailed issues (about each one), you can refer to the reference.