I have a 2001 Ford mustang V6 3.8 l the car itself on a idle above 4500 RPMs

Hello, with such a high idle speed, I would suspect a mass air flow leak, such as from a vacuum or PCV line, or intake gaskets leaking. Just a guess, but consistent with your concern. As far as the shifting - sounds like an internal transmission concern with that gear or torque converter function. Testing is needed to confirm the root cause of the concern and then troubleshoot further, but I'd say there's a fairly strong likelihood that it's an internal mechanical issue that will require transmission overhaul or replacement. Use this link to find some shops near you that can help with your concern: www.repairpal.com/repair-shops