if that was all that Christians believed about God, it would merely be an unusual definition of the word

In the words of C.S. Lewis: "Don't presume to think that I am saying more than I am." (OK, that may have been a bit of a paraphrase, but the idea is there). The only thing I was answering is the "who made God" question, and even then all I did was provide an explanation among other explanations of the "uncaused cause" question.

The other stuff you mentioned cannot be determined by science or logic; it is from divine revelation (the bible) that we understand that God is involved in this universe, sent Jesus to die for our sins, etc. And of course, we've already had that debate in this thread.