1) The restrictions that applies when a player controls 2 power are applied also for the activated major powers ?
From the Restrictions on page 12 of the Scenario book:
"Activated major powers conduct diplomacy normally making announcements and declaring war. However the restrictions for “Controlling 2 Powers” listed above apply between an activated major power and any other power(s) controlled by the same player."
2) During the activation of a major power if is possible for the activating major power to declare new wars (step 4 of the activation procedure). What about the DOW costs ? Are they free ?
If not they must be payed by the power that is activating the major power or the activating major power itself ?
They can't be paid by the activating major power itself since the latter doesn't get dealt cards until step 6 of the activation procedure (and in fact the number of cards dealt is affected by the number of cards in the hand of the power DOWed in step 4). I would assume the DOW is free. Chances are you had to invest CP in some diplomatic influence to win the resolution of diplomatic status in the first place.