88' Rx-7 problems

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So I bought a 88' Mazda Rx-7 some months back, didn't drive it for quite some time after that because I took a long time to get it registered. When I did start driving it though it idled rough, took a while to start, and had popping noises every now and then in the exhaust. So one time after work I tried starting it and it started up and then idled real rough, then when I tried to take off it died. I gave it an oil change, swapped out the spark plugs and spark plug wires, even gave it a new fuel filter. This fixed the problem of the rough idling and it not starting for now, then one day the exact same thing happened. So I thought since it was taking a while to start that the battery could be going bad, I changed the battery and the problem was that the battery that was in the car was not the one that should have been in there. It now starts up a lot quicker, but it starts and then idles at 400 unless I give it some gas then it kicks it up to 1500 and eventually comes down to 800 which is normal. Now I have been told that the reason it died both times is because it flooded itself, which I assume may have to do with me having to give it gas in order to get it to normal idle. Does anyone have any idea why my car idling so low in the beginning? Also does anyone know what the popping noise in the exhaust could be? I am investigating the EGR valve and the EGR solenoid, or it could be a a leaking vacuum hose some where. Sorry this is so long but I would really appreciate some help.