Rough idle and trouble hot starting
 

So I just bought a 1981 rx7 gs, and have some problems that you all might be able to shed some light on. First off it idles a little rough, almost like it has a very slight miss. It gives the engine a little shake every second or two at idle. Also there is a little surge when cruising at around 3000 rpm. In addition hot starts aren't the easiest. I have yet to be stranded but it usually takes me about 10 seconds of cranking with my foot hard down. And the last thing is there is a whining/scraping noise coming from the rear end that you can hear at slow speeds or coasting with the couch pressed.

The motor runs strong and will still put you back in your seat when you get on it. It only has 73,000 miles and it isn't the prettiest one I have seen but I only have 2000 for it. Being new to the rotary thing I am not sure where to start looking to solve these problems.

Thanks

Also, when cruising in fith there is a quiet pulsating hum and I can't pinpoint the location.