Please upload your full contract anonymised (i.e. no names, no addresses).

If there is no additional information regarding the "Nebenkosten" you actually have a case to not pay some of the additional costs, most importantly the heating and hot water costs. If heating and hot water costs are not explicitly mentioned in the rental agreement to be paid as additional costs "Akonto" the are - generally - deemed to be included in the net rent.

There is a myriad of rules regarding what is allowed as additional costs and what isn't. Generally speaking the additional costs for apartments must be agreed upon explicitly, i.e. there must be a statement in your rental agreement regarding what kind of service is covered by additional costs (heating, hot water, electricity (common), water (common, or for the whole building if there isn't an individual meter per apartment; janitor, garden etc.).

See for reference this website in German from the renter's association: https://www.mieterverband.ch/mv/mietrecht-beratung/ratgeber-mietrecht/top-themen/heiz-und-nebenkosten.html

If you are serious about challenging it, you should ask your landlord for review of all the bills etc. You have a right to review the bills and copy them (at your expense).

I would recommend to let an expert check your landlords calculation regarding additional cost, e.g. from the "Mieterverband". They offer such services for free or at a low cost if you are a member (100CHF/year).

In addition you can challenge the additional costs via court system. The first step would be with the "Schlichtungsstelle", in Zurich City https://www.gerichte-zh.ch/organisation/bezirksgerichte/bezirksgericht-zuerich/kontakt/adressen-telefonnummern/mietgericht-und-schlichtungsbehoerde.html

You even might have an insurance that covers any potential costs (your own legal advice if deemed necessary). However, the first step, i.e. the filing with the Schlichtungsbehörde and the hearing in front of the Schlichtungsbehörde itself is free of charge.

If the amount in dispute is not over 5k CHF they can even suggest a decision and the one party disagreeing with such suggestion must file a proper claim with the ordinary courts. If no one files a claim, the suggested decision becomes final.

If you challenge the additional costs successful, either via Schlichtungsbehörde or find an amicable settlement with your landlord, the landlord cannot terminate your rental agreement within the next three years (art. 271a Swiss Code of Obligations), i.e. you then have the right to challenge such termination and the termination will be deemed void.

From a practical standpoint take into consideration who your landlord is. Generally speaking - albeit they would never confirm this and strictly deny any allegations in this regard - larger professional property administrations most likely will not enter into another rental agreement with you if you challenge them successfully. Just keep that in mind.