Without a video of the smoke and more information it is not easy to diagnose...however,
if you have WHITE smoke and it does NOT stop smoking after warm-up, or gets worse, then
you most likely have an internal coolant seal failure and you are burning coolant
which is a common issue for 86 RX7s.
Also, Rotary engines do NOT like to sit for long periods of time....the o-rings, gaskets,
and seals tend to dry up. Hard to tell how the previous owners treated it.
However, IF the smoke stops after the car is warm, you may possibly just have a LOT of
moisture in the exhaust system and it is burning off. IF you have a different color of
smoke such as blue or black...those are different issues.
Having said all of that...the hard starting is the real problem, and you need to have the
compression checked to see where you are at. IF that is low, then it won't matter about
any of the rest of problems. All in all, it sounds like time for another engine...but I hope
for your sake it is something else.....
BTW....I have owned 9 RX7's over the last 15 years or so....they are great cars, but like
most things that are good...they require a good bit of care.