The shops in Fjällbacka are open at the weekends until Christmas. In January most shop keepers take a well deserved holiday to then come back and prepare for a new season. See individual shops websites or Facebook page for opening hours.
http://www.tangfjallbacka.se/
The fishmongers are open all year but with limited hours in the winter. Coop, the supermarket is open all year.
Valö Hotel and restaurang is open until mid October. Call 0046 705234330 for more information.
Fjällbacka youth hostel http://fjallbacka.bokarum.nu/?page_id=95
The post boat will take you on a stunning boat trip every working day, summer as well as winter. Call the day before to book you ticket, 0046 708421474. The boat departs at about 10.15 and costs 110kr/person.