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1. Go into Options – Colors – Body Background (Under Skin) and add your Page Background image there. (he has that named wrong, should be “Page/Site Background”).
2. I have my background image at 2000px width. And then I think you can select “Cover” for the image to expand to other sizes? Not sure on that. You’ll have to try a smaller image than your monitor size and resolution to see what the options do.
3. Having an image on “Homepage” only would be complicated and not something that the Theme developer would support. You need to Google and see if there’s any info on it. I’m sure it’s been asked before.