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I noticed in the history of the opponents turn that often as first step the enemy gains territory where I went away or just through during my turn.
My question now is whether the supply and production happens, before or after he regains control.
My guess is that supply happens first, but just want to make sure slicing with a scout between enemy units has the desired effect

You love your scouts   but hmm good question. If I understand you correct you mean like a scout moving by a unit then the unit gaining free path to supply by  its own zone of control some time of the start of the turn. Very interesting what comes first, zoc border push or supply movement.

Just checked myself. Supply is calcualted before ZOC moves the border! Go scouts

Test consisted of one infantery unit with 20 infanteries with 40 supplies before ending its turn. Then two scout units moved so that it had all squares around it as enemy squares but not behind it (an enemy infantery unit behind it again was set to prevent this.) The scouts move back again to its previous lines and hit end of turn. The infantery unit now had only 20 supplies and it was in contact with its own land due to it pushing its own border with its zoc. Conclusion, supply subtracts first then Zoc pushes border. conclusion 2: Try and encircle units 2 turns in a row even if they push border on theyre own turn and they are in troubles !

 If i am correct here, there would be no way of knowing your oppenent did this to you except for the loss of supply that you suffer. Cause the ZOC would push the border back before you got to see it in your turn.

You will have to watch the history log during your turn and also watch the supply level of your units carefully. Yes.

I have not used scouts yet. Seems like they certainly have their uses.

scouts are recomended, especially in large maps with little production. scouts at lv3 can carry supply for 6 turns and do antisupply, you can imagnine the havoc they can unleash upon enemy supply lines