Questions about doors (and vault doors)
Do I need to roll the dice to open a vault door? Or is it auto success?

It depends on the type of weapon used.

Vault doors can be opened like standard doors (unless otherwise stated in the Quest’s description)
Melee weapons with the “Open a door” symbol can be used to open a door next to the Survivor. Spend an Action and roll as many dice  as the weapon’s  Dice value: the door is opened if any die result equals or exceeds the Accuracy number of the weapon. Place a Noise token in the Zone.
Some weapons have the “Open a door” symbol without a die symbol on it.  They can be used to open doors without the need to roll any dice. Just spend an Action to open the door. A Noise token is placed if the weapon is noisy (see Reading An Equipment Card, page 12)



Can I close vault doors?

You can't normally close a door (of any kind), but there's a skill that grants the ability.

Lock it down – At the cost of one Action, the Survivor can close an open  door in his Zone. Opening or destroying it again later does not trigger a new Zombie Spawn.

It doesn't mention explicitly mention vault doors, but vault doors are opened just like any other door, so I would conclude they can be closed just like any other door too.

Vault doors can be opened like standard doors (unless otherwise stated in the Quest’s description)



It seems obvious that you should only put a noise token if the weapon is noisy for opening doors

I agree. This is already explicitly stated for weapons with the &quot;open a door&quot; symbol without a die symbol on it.

Some weapons have the “Open a door” symbol without a die symbol on it.  They can be used to open doors without the need to roll any dice. Just spend an Action to open the door. A Noise token is placed if the weapon is noisy (see Reading An Equipment Card, page 12)

(Emphasis mine)
I believe you will find there is no weapon with the &quot;open a door&quot; symbol with a die on it and without a bell on it. If you do find such a weapon, I agree that it shouldn't make noise when opening a door (although I'd check to see if the bell icon was accidentally left out first).