For the derailleur it sounds like maybe a rubber gasket got chewed up. You shouldn't need grease or locktite. What derailleur is it?
For the cogs, is it when the wheel is spinning and the cassette(all the gears) kind of gyrate around a bit? Cheap wheels can do that. But if you had a hard crash it's possible you bent the freehub body a bit. That's what the cassette attaches to.
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