I would go into PATS and try another Parameter reset , Erase all keys again , and then reprogram the 2 existing keys and make sure then enable add key feature . If you are able to get the 2 existing keys back to working  with add key feature enabled to work I think then other PATS keys cut should be able to be added  if you cycle the 2 working keys in the ignition and then the un- programmed  key will take. You should really never allow yourself to go under 3 working PATS keys , in case one gets lost. Then clone one of the working keys and put the chip part of it in the security bypass.

  

  usually when installing a remote start system there is no need to program anything, instead you just put one of the already learned key in the bypass system your installing but am unfamiliar with the system your using, factory or aftermarket since you didn't specified. another issue here is when doing a parameter reset, usually, not always your prompted on which module was replaced when performing a parameter reset and depending on the module replaced then the secret key is sent to that module to synch. autel's tools has always had that issue on some vehicles where the parameter reset is not set up correctly, and you never get prompted to enter the replacement module option which are usually IPC,PCM,TCM,BCM,SJB and maybe others. if this is a factory remote start system, there should be no problems, but if you are installing an aftermarket one, I will tell you from experience they don't work well on some fords.

uninstall that remote start system, leave it as it came from factory then do a parameter reset again, make sure the security light goes out and the vehicle starts, if that happens then your scanner is fine, install you remote start which most likely will want to have a programmed key in it, make sure its installed correctly. if it don't start after everything is back to factory then you have your answer right there, bad tool's software.

  well am not familiar with that remote start your using and I do no alarm systems either, I usually uninstall everything that is not factory equipment. but all ford needs is a parameter reset. I have used ford ids for more than 20 years and there is no such option/feature called synch. either the vehicle requires a parameter reset or not since not all ford vehicles requires it. in your case it does and its all it needs. on older vehicles like your it will say either ipc , pcm, bcm etc but not both, however on newer vechicles it could say pcm and bcm for example or ever 3 options but that is not really important to remember since there are so many of them and keeps changing but like I have said many times autel tools are not too reliable and your are going find your self in this situation many times. I do own a couple of autel tools that I only use for very specific things but nothing really to important. I charge a lot of money for diagnostic and cant risk a mistake like that. anyway am sorry I cant be of more help to you in resolving this issue and for the long post and by the way parameter reset is only performed after a module replacement and not in the event of adding keys, remote starts etc. consult the remote start manual for more info good luck.