Don't think I can help you with the heater but you might want to check and see if there is a steering damper on your car. It's like a standard shock absorber but mounted horizontally. Also check the front shocks.
I'm not really familiar with how they designed the newer Riv front suspension but if it's like my '80-'82 the steering damper is the most likely cause assuming that all the bushings are good.
The chain in the transmission is how the power gets turned 180 degrees to go back to the front wheels. It's a proven design since the '66 Toronado was introduced. They don't go bad too often (at least the didn't use to). You could have other internal problems with the trans. What your describing sounds like slippage.
Hope this helps.
Mark
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