I am writing a historical fiction novel that takes place in Kuusamo, Finland. How critical is it to get Finnish umlauts right for name places, etc.? Any editing suggestions?

I would suggest that you read some books by Finnish authors and see how they handle it. I just read a mystery by a Finnish author, and I can’t find it—too many books in my house—so I tried to find it online and discovered that there are so many Finnish mystery writers!