When the overlord is in play,

is it possible monsters can open and close doors? they should give up an action for this, which one?

we allways played it: monster open/close doors and give up either the attack/move action

Can overlord cards frenzy/dash be used to open or close a door. because you get an additional attack ACTION, or additional Move action.

normally the overlord only uses attack or move, so should i see these additional attack or move action also as an action when opening a door. or even trying to open a door (testing attributes)

example:

I lost (as overlord) the masquerade ball because lady Eliza kept failing her attribute test,

standing next to the door I tried 2 times (once for my attack action and once for my move action)

but can i try 4 times when using the "frenzy" and "dash" card?

Monsters are allowed two actions. The only restriction is only one attack action (no restriction about moving twice).

So monsters can move action twice.

Opening/Closing a door takes one action.

The second action of the monster is left to his choice.

Opening/Closing a door is neither a move nor an attack action, so dash an frenzy cannot be used to generate an opening/closing door action.

Page 11 of the core rulebook details all the different actions a monster is allowed to perform during its turn. Open/Close Door is one of them. Each monster can choose to perform up to two actions per activation from this list, with the only restriction being that it can only attack once. Granted, 99% of the time you're going to choose Move and Attack, but there are other options there.

You can't use the extra action granted by Frenzy to open a door, since that action must be "Attack." However, if you know you're getting an attack out of Frenzy, you can use your two regular actions to Move and Open Door, for example.