They both could be correct depending on what you want to express. Both are grammatical. the first says that there are no limitations on what you want to do, the second is a warning that there are limitations.

it depends, If you are studying English or or other Arts Subjects then Sky is the limit. If you are a science student then Sky is not the limit. ;-)

'The sky is the limit' is a common English expression, meaning anything is achievable.

Undefined. That's what my calculator would say.