MLB GENERATOR application

Ouch... that could be the problem... using Serialnumbers of original Macs should not be done and is also not necessary.
Do you mean a Admin Account or a Standard User?
On my machines the one user-ID I use is an admin, since I know what I'm doing... I think...

Send me your current config.plist and I'll check if I can see if anything's wrong with it.

That´s the reason!
Using cloned numbers of real devices you don´t own will always cause trouble since both devices try to register with iMessage and Facetime the same time. Numbers found on the internet are even worse since you will for sure not be the only one who found those numbers...
On Apples Servers it looks like the same machine tries to connect again and again with slightly different values and multiple AppleID´s it's no wonder they block this Machine and/or the AppleID´s which try to connect...

You do not have to do a new install... just add your config.plist in the next post and I'll check it for you.
Você não precisa fazer uma nova instalação... Basta adicionar o seu config.plist no próximo post e eu vou verificá-lo para você

Try the attached one, but make a copy of your original file, just in case...

Absolutely yes they are not meant to be changed!
Why do you want to change them?

Do not change this number, since all the other installed apps and services might lose their configs if you change this UUID.

I would first try to use iMessage and FaceTime without the UUID values.
If it works = good
If not = create new UUIDs and use them.

As I probably mentioned a couple of times before... I don't use manually created UUIDs on my builds.

You shouldn't contact Apple Support at all...
your issue is something where those guys can't help... Normally