Did you replace the sending unit with the factory original sending unit or the upgraded one that reads actual pressure? the stock unit is just an idiot light really it reads a set PSI and puts the needle in the center. If you bought the upgraded one then you also have to bypass the resistor on the back of the cluster to get it to read correctly. From your symptoms id say the synchronizer is the source of your rough idle but if the gauge is moving id say you got the aftermarket sending unit but have not bypassed the resistor so it doesn't know what to do with the signal its getting from the sending unit.
New DD-2009 Ford Mustang GT/CS candy apple red.
(sold)2003 XLT Tan 3.0L V6 5-speed, Lots of mods.