Speaking generally for the theistic evolutionist (evangelical) scientists I know (a fair few)...
Is it their belief that God existed before the origin of the universe?
God exists outside time, so God exists before, after, and to the side of the Universe.
What part does God play in their theory regarding the origin of the universe?
The Universe exists because God wills it so. The act of creation brings the entirety of the Universe into being - past and future included.
What part does God play in their theory regarding the origin of our solar system, and the planet earth?
Both are part of the entire Universe and are thus part of that creation. No direct 'tinkering' is required.
What part does God play in their theory regarding the origin of life on the planet earth?
As above.
What part does God play in their theory regarding the origin of man on the planet earth?
As above.
Is it their belief that God has intervened in the evolutionary process at any time (dramatic changes, complex organs, etc.)?
No, as it is unnecessary.
Is it their belief that God has intervened in the development of man to introduce an eternal spiritual presence that does not exist in other organisms?
Mixed - some yes, some as above. Those that say yes would typically consider a God, Adam, and Eve scenario similar to Moon-Watcher and the Monolith
Is it their belief that the miracles recorded in the Bible that contradict the physical laws of nature are true including the resurrection of Jesus Christ?
Most, yes - miracles being direct interventions by God that do contradict physical laws.