There are only several shops in Kihnu island. All are kind of similar. You can get basic food and drink there and some other things as well.
People in Kihnu love to sing. I would not be surprised, if you would hear the singing while you are just walking around Kihnu
There are national parties held in Kihnu, where people come together, sing and dance. If you want to get an impression of historical national songs and dances, you should attend one of those partys
Midsummer festival (23. June) is best oppurtunity to see this unique island's folk in their folk costumes and colours
Favorite thing: There are quite many junipers in Kihnu. Maybe not as much as in Saaremaa, but still you can see them in Kihnu as well and they smell good