My guesses are:

"When I start it up, the car idles fine at 1000 rpm, but if I then rev the engine a bit and step off the throttle, the revs go down drastically and the engine almost dies, on rare occasions it actually does but mostly they go back up and everything is fine. What is this?"

Dirty throttle body.

"at idle there is quite a nasty shaking. "

Vacuum leak. Many possilities but I'd look at intake manifold gasket and fuel injector seals. I located a bad intake manifold gasket on my car with a torch: open the gas (don't light it) and with the car idling pass the torch around all the possible vacuum leak spots. When you hit a leak the idle speed will momentarily increase.

Terry