Mormons pray to the same God that Jesus prays to. Remember Jesus told us that his God and his Father is our God and our Father (see John 20:17). We are brothers.
'All' first Christians did not have the bible we have today. Even all Christians did not have the same bible we have today until the 4th century.
Jesus read the OT, not the NT, it did not exist before he was resurrected.
JS does believe the bible says 1 God, but he interprets that to be 3 Gods that are so unified in Their salvation of men, that it is as if They are 1 God. That is the only interpretation that fits all the descriptions of God and Jesus in the bible, the whole bible, not just a couple of scriptures that you cherry pick to prove your point.
Remember, JS saw them.