I like
Frederica but prefer Frederika. I went to school with a Frederika but she spelt it
Fredrika. Unfortuantely she was not a very nice person so I don't have great associations with the name. Personally I prefer the spelling without the "extra" E. Fredrica or
Fredrika (just as I prefer
Fredrik to
Frederik) Overall I think it is a nice name and definitely useable.