"This fish is white!"
Translation:Ta ryba jest biała!
No. You cannot use the "to" construction if it is followed just by an adjective.
You may think of this "to" a bit as if it was an "=" sign. If you say "This fish = a white animal", it's okay. But you can't say "This fish = white".
More info here, especially part three: https://www.duolingo.com/comment/16373167
Yes we do. Many people from Russia or Ukraine tend to do it when they speak Polish. Even if they language is nearly perfect usually skipping „być” too often reveals that they are not native speakers.
We can skip „być” when in complex sentences when only one is enough:
Ta ryba jest biała, ten ptak czarny a to drzewo brązowe.