I just got a 87 fc rx7 it has 110k miles on it only 2 owners well taken care of but assoon as I got it home it started idling bad around 500-600rpms then dropping to 300rpms and sometimes dying, I noticed there was a belt missing for the air pump once I put on a new belt it started backfiring just a tadbit and the rpms sat at 1000, sometimes dropping lower to 700 this is my first rotary so I'm not very knowledgeable about them in hoping its not the apex seals but I wouldnt know

 

Start by downloading the Factory Service Manual (FSM), and whenever you get a rotary car, first thing to check is compression. A normal compression tester can be used if you remove the Schrader valve from the hose so it doesn't hold pressure and watching the blips as you crank the motor (with egi fuses pulled).
Also, the car should idle when warm at about 750rpm