A majority of shops are closed on Fathers' Day, Sunday November 9. Shops smaller than 100 m2 or stores in sparsely populated areas are not be affected by the holiday limitation; larger shops in these areas will close.
All Alko outlets and banks are closed as well as most post offices.
As for public transit, you can check the timetables of long-distance buses here, Helsinki transport services here and rail schedules here.
Finland started observing Fathers' Day in 1949 and as an official day to fly the Finnish flag in 1979. Nowadays it is celebrated annually on the second Sunday of November.