duży = big for masculine nouns. (pies is "on" in Polish)

on(he)-duży
ona(she)- duża
ono- duże

No, the word "pies" is just grammatically masculine, so it always will be "duży" if you decide to use the word "pies" spefically. Even if you do know that this is a female dog.

On the other hand, you can possibly refer to the dog as 'she', and say "Ale ona jest duża!" (How big she is!), for example.

Well, "wielki" is not exactly "big", it's more. I don't know if it has a really good translation... we translate it as "huge", but then it seems too much. So I'd say big < wielki < huge ;)

Yes, but that's not an exact translation. "wielki" doesn't have a good equivalent in English, it seems more than "big" but less than "huge"... this course treats it as closer to "huge".