1) if you want to unlock the phone, get a code and unlock the phone while running a stock ROM. You will not be able to enter the code using a custom ROM; and
2) do not attempt to downgrade the bootloader. Any attempts to downgrade could, and probably will, brick your phone.
I doubt it. If it did, there would be a big thread about it in the i747/i747m forum. Also, under FAQ, it states the following: support international Galaxy S3 i9300 (Us qualcomm based GS3 are not supported at this time)
That unlock app will not work as it does not support U.S S3 variants
There's a working downgrade to 4.1.1 check it out and while on it, try the free unlock then upgrade again
Edit: my bad.. You can't do the free unlock even of you downgrade because the bootloader is still 4.3... Only way to do it once you're on 4.3 bootloader is to purchase an unlock code
Good luck
Sent from my SAMSUNG-SGH-I747 using Tapatalk