No. Mace Windu's lightsaber is a fictional weapon from the Star Wars universe which has its own set of rules like being powered by a kyber crystal and being used by Jedi. Pulp Fiction is set in a more realistic, albeit violent, modern world where such a weapon doesn't exist.
There is no direct relation between Mace Windu's lightsaber (from Star Wars) and Pulp Fiction. They are from two completely different fictional universes with no official crossovers.
I think Hermione would be the most likely. She's very intelligent and a quick learner. She would study all the available information about lightsabers, probably find some ancient texts in the library about similar weapons. With her determination and knowledge - seeking nature, she'd be able to master the basic techniques of lightsaber handling in no time.
Well, perhaps Harry discovers an ancient magic that allows him to wield a lightsaber. He could use it to fight Voldemort in a more unique way, combining the magic of the wizarding world with the power of the lightsaber. Maybe he has to go on a quest to learn how to master it fully.
Obviously, Voldemort could still be the main antagonist. He would be intrigued and threatened by Harry's new power, the lightsaber. Also, some Death Eaters might team up with dark wizards from other lands who are also after the power of the lightsaber.
Palpatine is often involved. Since he is a master manipulator in the Star Wars universe, he could be the one who subtly guides Windu towards the dark side. He might offer false promises or twist Windu's sense of justice to make him question the Jedi way.
Well, in theory, it could. Fanfics often like to blend different fictional universes. However, in the official Harry Potter lore, there are no lightsabers. But in a fanfic, an author could come up with some creative magic or a cross - universe event that brings lightsabers into the wizarding world. Maybe a powerful wizard discovers a way to create a weapon similar to a lightsaber using magic and some rare materials.
He could find it during one of his missions. Maybe he's exploring an ancient ruin and stumbles upon the lightsaber. It could be in a chest or just lying there, and Naruto, being curious, picks it up.