So do you still have to pay the €3 to keep a card you have drawn by using an action or ability of a card. Example: Restricted Area: Spend 2 to draw a card. So do I spend 2 to draw the card and then another 3 if I want to keep it???
It will say so on the card. If it just says to "draw a card", you keep it for free, like with Restricted Area. The same is true for any instance you see that black project card icon (on cards or as placement bonus on the board).
In contrast, for instance Business Network tells you to "look at the top card and either buy it or discard it" (and doesn't show that project card icon).