Does this mean that if player2 with upgrade level 1 gives a marine (e.g. via a trigger), to player1 with upgrade level 0, that marine will automatically 'downgrade' to level 0?
If the upgrades do stay for the specific unit being given, then something like a madness map could create units for a comp with some upgrades, then give those units to the desired player.
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Tell me more about that please, it interest me, what AI sccript ??? I'll give a karma to the one that answer me

I ever download a map by heimdall but it didn't worked on well, ....
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There is no AI Script that does automated upgrading. There is however an AI Script list in the tutorials! That might help.