Also the rules in section 5.2 show an example of NATO being played before the marshal plan or the warsaw card. How can that be correct if the NATO card says that you cant play this card until after the marshal plan or Warsaw?
You can play the CARD (for op points) but not the EVENT before it is eligible.
This is one of the best things that can happen to you when you have an opposing side's event on a card.
Note the following in rule 5.2:
If a card play triggers an opponent’s Event, but that Event
cannot occur because a prerequisite card has not been played,
or a condition expressed in the Event has not been met, the
Event does not occur. In this instance, cards with an asterisk
Event (marked *) are returned to the discard pile, not removed
from the game.