My general Rule of Thumb - If you don't own it - don't use it. That includes "parody", "fair use" or whatever you want to call it. If you don't have a clear legal chain of title to a property, you won't be able to distribute it, sell it, etc. From my point of view, its more creatively satisfying to make something new - my own unique expression.
When I see a "Star Trek or Batman or (name any superhero) Tribute Video", I can't understand why, with the amount of talent and creativity evident - why they don't make an original work? I understand the concept of a calling card - but an original work - while it won't get the same number of online hits as a Batman-parody - would be just as good.
Let's put it this way. Assume you're a huge Joss Whedon fan. If you had the opportunity to meet him, would he be more impressed if you made:
A) An exact 10' long Lego replica of Serenity from Firefly.
B) A short ORIGINAL video - and tell him that he inspired your creativity.
Let me save you some brain-power. Ive been there. You will have a much better conversation with your creative idol - a "conversation of equals", if you choose Option B. Trust me on this...
ABOUT THOSE LEGAL QUESTIONS: I am trained as an Animator. I work as a Writer/Producer/Director. I am not a Lawyer. I am not qualified to answer legal questions. Nor am I qualified as a Dentist or Nuclear Physicist.
If you have legal questions - ASK AN ENTERTAINMENT LAWYER!