Nothing, other than which issue is which.
Links are directional, which is why you have two descriptions for each link type - from one end of the link "X duplicates Y" and from the other end, "Y is duplicated by X". It's telling you which one was the original in that case.
Absolutely not, that would be an utter disaster for most links. Links are for information about how two issues are related. What you're asking for here does make sense in some cases, but not in most of them. Read the list of default link types and just think through what they mean.
To get you started on that thought, take the case of "AAA-5566 is a duplicate of BBB-123". I deliberately close AAA-5566 because it's a duplicate. There's no chance I want BBB-123 to be closed because I've closed a duplicate - the whole point of what I'm doing is BBB-123 stays open!
I think it's about 99:1 - in 99% of cases, you don't want a change to update the other end of a link. In 1% of cases, you do. Because of that ratio, there's nothing in JIRA that will do it, but plenty of add-ons that can if you do need it (and those all enable some form of "if X, then update other end of link)
It tells inward and outward description of the link types. See <your host machine>->admin->System->Issue Features->Issue Linking
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