Might be the same as me
Hey man. I have something similiar. I back out to the left when leaving my driveway. If I cut my wheel almost all the way to the left in reverse I will get what feels and sounds like a little bump roughly every rotation of the tire...no matter how slow I go. I can also feel the steering wheel pull just a hair at each 'bump'. If I cut it ALL the way, I get the squeel/rubbing sound but I know that is the tire/rim rubbing the swaybar. I have the Steeda swaybar and 275/40-17 tires so I know they touch. I can get that in forward also but the 'bump' only happens in reverse. the 'bump' also does not ALWAYS happen. Just sometimes. Ever since I put the suspension stuff 0n my car I get all kinds of occasional sounds, squeaks and other noises. I know it is all on there correctly, tight and aligned AND I also know I can go out and hammer the piss out of it and it does not budge a hair so I guess it is just the parts and the fact that it is a Ford.
My rearend is making a sound when I let off the gas in gear and then press back down on it....like there is a lot of slack somewhere and not just the standard slack of the ring and pinion. Now again I haved Steeda Hght adj LCA, Dble adj UCA, sport springs, adj rear swaybar and aluminum drive shaft. Is it any of that? I don't know but I have double and triple checked every bolt and nut and part I put in and can not find anything loose or installed wrong. But I can pop that gas peddle and make it sound like the rear or something is about to fall out. Kind of sounds like it comes from the transmission area too in a way. Who knows.
Anyway is yours stock? If so take it to the dealership. But that can be a WHOLE NEW NIGHTMARE. Otherwise drive the hell out of it and have an emergency fund ready to cover the damage. That's what I do.