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"""(first question, is there a difference between a rebate and cash allowance and/or cash-back?)."""
They are all the same, generally rebates and cash back monies would go to the customer while the dealer would use the rebate as a cash allowance and knock that off the price of the car instead of you receiving the cash and Yes, you can use the rebate as a down payment in most cases, If you keep the cash, you're basicly financing yourself a personal loan, If you use the money to knock the price of the car down, then (depending on your credit) you'll likely need to come up with a down payment as the stealer keeps the ash allowance.
In todays automobile buying environment, you'll find dealers are swerving all over the road (like a drunk driver) in the deals they'll make.
Dig around and educate yourself as to what the current lowest prices being advertised on the vehicle your looking at are, I've been looking at 2009 Mustang GT's and that car hasn't been selling at all over the past six-months so the Dealers are making some very good prices on one right now,
I also made the mistake of visiting a Dodge dealer and pricing out a 09' Charger R/T last week all I can say is WOW!!! Now I know what it feels like to have a bunch of shrks going into a feeding frenzy, Those guys were brutal and actually did make me a far price, Unfortunately it wasn't good enough as I don't think Chrysler will be around in six months,,,
I'd use cars dot com and the on lne auto trader to find the lowest advertised prices for the car you want.
Good luck,