Mysterious squeaky sound
Hmmmm, it sounds like (to me) that you may have a spacer missing behind the cassette on the freehub body for the whole thing to be moving a bit. Also try unscrewing your high limiter screw ever so slightly (about a quarter of a turn) just to see if the noise starts to disappear. (Note, you'll have to change gear and then back in again to get it to deadzone as I call it.)

(I usually call the highest gear a dead-zone gear because there is no force from the cable acting on the derailleur to keep it there, making it rest against the limiter screw.) 

It may or may not also be from the derailleur jockey wheels being so far away from the cogs; Has your B-tension screw been set accurately? The tooth of the jockey wheel should be about two millimeters away from the cog when it's on the lowest gear, depending on where you're looking at the reference point. I'd personally reccommend taking it to an LBS if you still can't figure it out; It can take a fair bit of experience to try and diagnose things like this, but if you're not face-to-face with the problem, there's not much that can be gleaned from this. What you perceive as a tapping could be a ticking to me. Or a squeak could be a squeal. It's how each person would personally describe a sound, which is what makes online assistance hard.

If you want to test to see if it's the spacer that's causing the problem as a temporary check method, get a pop bottle, cut it and lay it flat, cut a circle the correct size to fit on the freehub body and test it. 

Actually, whlist you're at it, check your rear derailleur hanger; if it's out of whack slightly, it could mean something is rubbing where it wouldn't normally, and may not be to do with the hub at all. (Though, the cassettes moving still does cause concern.)

When reassembling the cassette onto the freehub body, I redidculously highly recommend using Lithium Grease on each component, between where each plastic spacer meets the cogs of the cassette. This grease is very, very light, does not clump as much as others, and is very handy for the fact it's bright white, so you can clean it off of your brake components if ever it flicks, which it shouldn't if you put a thin layer on. :)