Do I have to use a travel day for domestic transport in Switzerland

Its valid if you have a active travelday :) 

And you have to log each train to your traveldiary.  In General all "free offers" like for example the shiprides on Lake Thun or Lake Brienz need a travelday :)

Discounted ones like the train from Interlaken to Grindelwald/Lauterbrunnen  (25%) need no travwlday 

And with a Eurailpass not everything in Switzerland is included For example no Postauto (Bus) or Public transport in the City öike Tram or Trolleybus or the ships on Lake Leman und Lake Lucerne are not included :) 

There is a swiss own offer called SwissTravelpass this Covers wide more than Eurail in Switzerland. 

I can say that swiss conductors are one of the best informed about the different Railpasses 

I recommend to read the rules carefully otherwise you can get huge fines in Switzerland for traveling without a valid ticket. Here you can check the different Validityroutes of Interrail/Eurail and other swiss offers (for example Eurail includes only 2 Postauto (Swiss word for Bus ) lines ) SwissTravelpass includes wide more 

https://www.sbb.ch/de/bahnhof-services/am-bahnhof/bahnhoefe/karten-bahnhofplaene/trafimage-karten.html