Usage of "before" in "I watched the sequel before the original movie"

Yes. "Before" serves as a correlation/correlative conjunction and functions like a coordinating conjunction in this case, which would allow you to omit repeating the SV.

Sounds fine to me.

Before can be a preposition, a conjunction or an adverb.

Before watching makes it a clearer case for being an adverb, whereas before the original makes it a clearer case for being a preposition. Regardless of the part of speech, it's correct.

The Oxford Learner's Dictionary has some pretty good examples, some of which are pretty similar under the preposition entry, such as "He arrived before me," where an object pronoun comes into play even though you could just as easily say "He arrived before I did."

If you're set on finding an alternative way to express it, try something more concise like "I watched the sequel first."