When I make a trigger: give one Terran Machine Shop to an other player, it doesn't work. Is it because it's impossible to give Terran Machine Shop to other players?

is the machine shop owned by a player in the game or is it neutral?

Sounds about right.

You can preplace unattached add-ons for any player and move them around (I think) but you can't give them.
Unattached addons are always P12, attached ones always belonging to the player that owns the main building.
So you have to give the main building and the addon will "follow" the player change.

You can give the attached factory to the player. If, for some reason, you hate the idea of having the factory next to the machine shop, you can preplace and link the machine shop with the factory, but spread the link out far away, prevent the player from viewing or selecting the factory (preplaced in a corner probably in order to prevent lifting) and give that factory.

Since pre-placed addons are player controlled, couldn't you have 'Player to give addon' have and addon pre-placed at a location- then have 'Player to recieve addon' with an addon "off-arena", then swap the giver's addon for the reciever's?