NO, but they can do so before taking over as master/ch eng or after officially handing over they ca carry out ISM audit of ship.

Yes a cross depratmental audit can be carried out. If such provision is included in the company procedure it can be treated the same as an internal audit. 

So effectively the CE can audit the Deck and preferably the Chief Officer can audit the engine. I would not encourage the Master to audit as he has to be the receipient of the results and the person confirming the rectification of observations.