1. Does it mean the writer is dreaming about California so the fact is that he is not in California? Yes - that is made clear with "If I was in LA".
2. Is it OK to say, "Alberta dreaming" meaning I'm dreaming about Alberta? You could - it wouldn't have the same emotional appeal.
"I passed along the way"
3. Does it mean 'I walked along the hallway'? I walked down the street.
"You know the preacher likes the cold"
4. I wonder why the preacher likes the cold weather? I think this is a line put in to fill a metrical need and to emphasise the singer's sense of longing for the warm climate of California.
"If I didn't tell her, I could leave today."
5. What does the quote above mean? Is it a subjunctive mood? I would be able to leave today if I didn't tell her I was going.
The Song California Dreaming lyrics - California Dreaming