As a native BrE speaker, I would probably say Is it anything to do with this? (or "something" - they're normally about equal and interchangeable). But AmE does seem to favour get in such constructions.
Per @Jay's comment, OP's versions #3 and #4 are dated/formal (archaic is putting it a bit strong).
In some related contexts, there are different implications regarding anything/something. For example,...
"I hear you found a dead body near my house, officer..."
"...is that anything to do with me?" (implies denial of involvement - "It's nothing to do with me")
"...is that something to do with me?" (implies a genuine enquiry - "Is it someone I know, perhaps?")