Just bought a 88 RX7 FC3C
 

New to this whole rotary thing and my 88 FC3C n/a being my first car I don't know if it has a idle problem but from a cold start it revs up to 3k then down to 1 and keeps doing so for about 15 sec. Don't know if a problem or just natural for a rotary. Won't pass smog and don't know why, has o2 sensor but I'm thinking if changing it out and seeing what happens. Like I said this is my first car and I only had it for about 3 days.

A cold start (coolant temps above 60) should result in the high rev 3k for 17 seconds and then it should drop to about 1500 and then slowly drop to close to 800 rpm as the engine slowly heats up. If it fluctuates between the two values provided by you for 15 seconds and then stops then there is a bit of an issue.