Yes you can. On the standard dreamhost plans, you only get one free lifetime domain registration so you'd have to pay for the second domain registration (or sign up using a promo code that gives you extra free domain registrations).
Yes, you could do this with either mod_rewrite or using the DreamHost transparent proxy mechanism.
I'm not quite sure what you're after in this situation. Why do you need two different index files but the same site content? This seems to be contradictory.
Hey, you'll find everyone here more happy to answer your questions. We may have to ask for some clarification at times, though!
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