Ok, so it would appear that this trans may or may not have the actual mileage and who knows what happened to it prior to you getting it. At this time, I guess you only have 2 options.
1. Drop the trans and rip it open to determine what is going on.
2. Take it to a shop and have the same thing done. Either way, its gotta come out.

Oh well, not what I wanted to hear (well, read!) but at least, that'* a fair and honest answer!

Thanks a lot for your time, it'* greatly appreciated in a world where no one gives a flying F about anyone else!

Quick question : Will ANY 4T60 from ANY GM so equipped vehicule fit? (I don't care about gear ratios and all, just fitment)

Yes and no. Try to stay as close to your year as possible. You will see why on page 10 of the 4T60-E ATSG manual...
http://www.kc2jga.com/4T60-E.pdf

Again, we please ask you to put your YEAR/MAKE/MODEL/TRIM and ENGINE in your signature like I have in mine. This can be done in the User Control panel at the upper left corner of the forum.

Thanks for the link and I've did the signature thing.