For a comprehensive answer to the cross, look here:
http://www.newadvent.org/cathen/04517a.htm
This is a Catholic site so might be regarded as partisan (despite the plethora of non-Christian sources).
If you need more evidence, search 'archeology of the cross' or suchlike under Google.
Short answer:
The cross, as a means of execution, was used throughout the Roman empire. Never by the Jews, and rarely by the Greeks.
Its origin can be said to lie in the early practice of hanging from/on trees, but in Roman hands it became a terrifying method of torture. In basic form it was a stake set in the ground, to which the victim was obliged to carry the crossbar, which was then fixed to the upright. A message was sometimes fixed atop the upright detailing the offence.
It would seem the biblical account of the crucifixion describes the practice in its most common form; the victim was tried, condemned, flogged, made to carry the crossbar through a jeering crowd to the place of execution, then crucified.
The Trinity?
"The mystery of the Most Holy Trinity is the central mystery of Christian faith and life.
It is the mystery of God in himself. It is therefore the source of all the other mysteries of faith, the light that enlightens them. It is the most fundamental and essential teaching in the "hierarchy of the truths of faith". The whole history of salvation is identical with the history of the way and the means by which the one true God, Father, Son and Holy Spirit, reveals himself to men "and reconciles and unites with himself those who turn away from sin".
Catechism of the Catholic Church, 234 (my emphasis)
Thomas