Where to begin
 

We recently purchased a low km 79 Canadian SA auto for my 14 year old son. I don't really have any history on the car other than what I was told. The story goes that the original owner asked his neighbour to sell the car for him. It went to auction where a friend of mine picked it up for his son. They buy and sell cars for a living so he had it since May of this year but then was given a 300Z by his Grandfather so they put this one up for sale.

The car the day we picked it up.
https://cimg4.ibsrv.net/gimg/www.rx7...35f4be9c28.jpg

Here is where we are with the car. It is 100% stock under the hood.
- Starts fine when cold but only using the choke
- Backfires until it warms up
- Seems to have a bit of a rough idle (Almost like a misfire)
- Many oil leaks (guessing from lack of use)
- Tach fluctuates
- Tripometer doesn't work
- rear end has a leak and clunks when shifting at slow speeds
- the worst part is the only radio station that comes in clear is country music

We have never owned a rotary so I am new to all of this. Should I start with plugs and timing or at the carb for the backfire? Or could that be caused by an exhaust leak? There appears to be some tape around one of the pipes but I'll have to get it up in the air to confirm.

Pic of under the hood.

https://cimg7.ibsrv.net/gimg/www.rx7...8eee6a3cb1.jpg

Any idea what this connector is for?

https://cimg3.ibsrv.net/gimg/www.rx7...320ae48f31.jpg

Or this one?

https://cimg3.ibsrv.net/gimg/www.rx7...5b68de14b7.jpg