rough idle, misses while accelerating

here is the back story.
traded my nice 2001 4.0L cherokee sport for a 1995 mustang GT 5.0 and taking it around the parking lot it ran good. we traded and on the 1 1/2 hour drive home i noticed it had no power and missed like chugged like crazy. thought it was timing so got it home and they didnt take the inhibitor when they timed it so i took the plug off and timed it 10 degrees and it ran better but still has a rough idle jumping from about 550 to 950 rpm. then when accelerating it intermittently misses and chugs but at highway speed if your foot is steady it drives just fine. any ideas? i think he said he did a egr delete (idk where its located so pics would be nice but i think its under the intake) but there is a hose in the back just chilling and making sucking sounds. ive been told it might be slack in the timing chain or the chain jumped teeth. ideas? also it has headers now
 
I suspect the MAF sensor hasn't been cleaned in years. Get some MAF cleaner and clean the element (it's fragile so be careful if you plan on using a q-tip). You will need to remove the MAF from the air intake to get to the element. Also, clean and check the battery to engine and engine to chassis grounds. These need to be solid as all the engine sensors require good grounds to function properly.
 
is that hose that is just chilling hooked to anything or is it just sucking open engine bay.....sounds like a vacuum leak....
94-95_Mustangs_Vacuum_Schematic.webp
 
I second the vacuum leak theory. A vacuum leak on a MAF car amounts to unmetered air entering the intake. I had a similar situation on my '02 GT. It got so bad before I finally found it that it was running rough enough that people thought I had aftermarket cams installed; it was running incredibly rich as well. Buy a set of vacuum caps from the Help! section at the parts store and check that theory first. Cheapest and easiest solution.