1995 Honda Civic Car backfires no exhaust

I got a 95 civic and the exhaust is straight piped, about half way back. I know that needs to be fixed, but im wondering if that will cause the car to backfire, and sound almost like a dodge srt4 on deceleration, also when I gas it heavily, it breaks up and like cuts out, and then when I press the clutch, the rpms go down, and it will idle at like 300 rpms, then once I come to a stop, it will idle low, then itll go back up and idle normal.