Notice what's missing in that description?
Superman.
A world with Supergirl but no Superman...I dunno....
(The BBS's spell-check agrees with me...as I type this, there's a red squiggly under her name, but not his....)
Possibly. I remember the original show description (seen in this older article I found) talked about the powers she shared with "her famous cousin":
http://deadline.com/2014/09/supergirl-tv-series-cbs-dc-greg-berlati-ali-adler-836682/
But who knows if that's still the case. Personally I don't see why the character couldn't work just as well all on her own.