I've read the answer listed here, but I still have a few questions. When a question is marked duplicate, it is marked with [Duplicate], but what does that do? (For reference check this question.) The question is marked as [Duplicate], and no Answers can be added, but other than that, no changes are made. Edits can still be made, comments can be added, and votes can still be made. I have seen questions that have been marked duplicate that quickly disappear and I guess my question is why some of these questions stay on the homepage for an extended period of time instead of just getting closed permanently
It depends on your definition of "closed permanently", but before being actually closed any question gets put on hold first, to allow the OP to edit, change, ... its question to allow it to be clarified as it might not be off-topic/duplicate/...
After the 7-day grace period of on hold, the question gets closed and after a number of months of inactivity, soft deleted. (Nothing ever gets deleted: it still stays in SE's database forever)
However a duplicate question is a special case as it acts like a pointer towards another question. So sometimes the duplicate generates more initial views then the original and deleting the duplicate from the site would be counter-productive as otherwise someone else might ask the exact same duplicate.
Just to give a hypothetical example: "How does hibernation work?" might be a good question with an excellent answer, but "My hibernation doesn't work!" is a duplicate of the former and unfortunately, that's what most people type in google, so they get re-directed to the correct answer!