The accuracy of altimeters appears to be more a question of certification standards, and I very much doubt there will be any ICAO standard or recommended practice (SARP) pertinent to this question. From the operational point of view an altimeter is fine when it indicates the elevation within the tolerances given in PANS-OPS, Volume I, Part III, Section 1, Chapter 3, Section 3.2. At least this what ICAO requires; of course Bloggs has already mentioned national requirements which may be different.
With regard to your question concerning the definition of 'QNH' your assumtion is very close to the definition in PANS-OPS, Volume I, Part 1, Section 1, Chapter 1: 'Altimeter sub-scale setting to obtain elevation when on the ground'.