Thanks! Bob's information about the TY395 engine, the Tang drive and the links for the hydraulic pumps helped me a lot. And Piper184 was right, it looks like a Jinma 284 (same logo on tranny and seat) and some of them pretty much have the same hood. But from the pics I saw, they look smaller than the KJT 6030. That KJT has the size to be a 60HP tractor but you're right, this 3 cylinders engine (which should be 1.5L) isn't big enough to be 60HP. 40HP is a good guess.
Here is the plate on the engine. I haven't found anything with the informations on it so I forgot about showing it here.
I could show you a picture where we can see the decal on the hood but KJT 6030 is the only thing written there. As for other tags, plate or anything helpful on the tractor, believe me I searched all around and found nothing except that date on the tranny you already saw (no tags on fenders, frame, engine block or anywhere else):
I was there when we took the hydraulic pumps off and there was nothing written on it too (I can trust my eyes on this) but what I saw on CircleGtractorparts.com let me think the pump we need is the E314 in this link:
CBN-E314 Hydraulic Pump (old style) For TY395 Engines
They even sell that cross connector that got lost with the pump:
And one of these diagrams to show where this pump is used REALLY looks like the hydraulics on my friend's KJT:
So pretty sure we're on our way to something. Thank you! I'll get back to you once I get something useful to write.