Did Jesus die on a cross? Does it really matter? It doesn't change anything that I can see.
While it's not a salvation issue, in an indirect way it can become one. This is an uncharitable view, however I do think one of the main reasons the Watchtower adopted the torture stake view was to cast Christendom in a dishonest light. It emulates the old sales line of "You can't trust them but you can trust us!". If the church is lying about the cross, what else are they lying about? If the cross is pagan, what else is pagan? This is exactly what the WT want it's congregation to think.
It's easier to convince people that something is true if you can place doubt and distrust in the mind of the individual. In the case of the watchtower, if their congregation are led to believe that Christendom is corrupt/pagan and so forth, then this forms a very powerful deception around the witness, who's access to the truth is largely cut off. It's why the bible says test all things (1 Thess 5:21). There's a very obvious reason why the WT have their own translation that is at odds with virtually all others.
A good hermeneutic is paramount to interpreting scripture. It's not enough to look up the greek word Stauros and use that as the basis for saying He died on a torture stake. There is a clue in John 20:25, when Jesus appeared to Thomas and said "Look at my hands..", plus the sign was described as being above his head, not his hands. Lastly, it's always good to study history and read about the common forms of crucifixion imposed by the Romans.
Is god a trinity? Again, who cares? Jesus still told us to pray to our heavenly father.
Without discussing the Trinity, the most important theology is that of Christ. In John 8:24, he said that if you do not believe that I am he you will die in your sins. Very strong statement, but one that needed to be said, as He knows that how people view Him directly affects their relationship with Him and therefore the Father. He made it clear that to reject Him is to reject the Father. He also asked Peter "Who do you say I am?"
Yes we do pray to our heavenly Father. We can also pray to Jesus ( John 14:14, 1 Corinthians 1:2, 1 John 5:14, Acts 7:59 ). I've read some of the JW articles and they forbid praying to Jesus, even though the Word of God disagrees with them. Who is our final authority? God or man?