How to insert bulb in this fluorescent socket?
Yeah, that's just a wacky "feature" of this particular type of tombstone.  

Yes, that little black sleeve rotates independently from the white tombstone.   In theory, it's supposed to be impossible for it to be in that position - since you would have had to turn it 90 degrees to remove the tube.    However, if the tube broke or was cleverly removed in some other way, it could wind up like that.  

So, you need a "key" to turn it 90 degrees. The key looks exactly like the end of a fluorescent tube, and I bet you have one of those :) You just stick the tube almost into position to install it, and land only that end on that tombstone.  Turn it 90 degrees (should be a small detent) and you're all set.