I bet the source of the problem is the gear setting. Can you check the contact pattern, snap a picture and then post it?

can someone just tell me how to check if the locker is not defected?
i want to perform a test while the locker is installed in order to determine if the locker is defected or the installation is incorrect.
the test in the manual, I'm unable to understand it.
the locker is making noise even when the shafts are not installed so all i need to know is if the locker does locks itself or not, because if not i need to send it back to the U.S and then I'll be in big trouble.
please help I'm losing me mind here.

anyone?

I've reached 2.70 in the backlash, it's not right is it?
by the way will i be able to get anywhere by opening the locker?
will i see spot anything wrong if something is messed up in there?

Somthing is not right here , theres no way you have 2.70" as a back lash setting. Unless that is some sort of metric conversion. The back lash on a 8.5" GM ring and pinion should be between 0.006"-0.010" inches.
Also your noise is not coming from the locker , just from reading back 4 pages I can tell you its coming from your ring and pinion. Also checking a wear pattern with paint on a used gear set up only works if you look at the coast side of the gear , which should be explained in your instructions. You cannot put a full locker like you have done into a differential without at least checking backlash and carrier/locker/side bearing preload. If the noise is as loud as you describe it then your ring and pinion is probobly shot. You can make an attempt at getting the set up where it needs to be but it will probobly have a 'whine' or 'howl' noise to it upon accelleration and/or deccelleration until it is replaced.
The normal noise that a rachet style Detroit locker makes is usually only heard while turning in a parking lot , low speed -sharp turns.
Hope this helps you .

Even with the metric conversion 2.7mm = 0.106" which is WAY to high for your backlash which should be as stated above. When I asked about your gear pattern, you must not have checked it because 0.106" worth of back lash would result in the gear pattern cutting off somewhere towards the middle of the ring gear tooth instead of nestled down in the root of the tooth.

I am betting that you just need to redo your shims side to side to get the backlash down to the aforementioned values.