Hello Quoiberau97
1) Can I use my Saver Day Pass to take the EuroCity train to Milan?
YES, but you need a Trenitalia ticket from Chiasso to Milan in addition.
2) If I can board, do I just buy tickets for the sections not covered by the Saver Day Pass?
See 1).
3) I know that seat reservations are mandatory on EuroCity trains.
For example, if I have booked a ticket and seat from Chiasso to Milan, is it okey to take the train from Arth-Goldau to Milan? If I can, so where should I sit?
Seat reservations are mandatory for the Italian part only. The seat reservation comes automatically if you purchase a Trenitalia ticket. You can occupy the seat starting in Arth-Goldau, provided the seat is available. Otherwise you can swap seats at Chiasso at the latest.
I, personally, would not use a Saver Day Pass for that route but rather purchase a ticket for the whole journey, including the seat reservation.
Kind regards,
Roland