Andy wouldn't worry about the 2mm gap it's just the frame thats out of square which doesn't mean a lot. More important that the x axis gantry is square to the Y axis rails and the y axis rails are parallel to each other.

The Y axis doesn't look to be binding too much but it does look and sound very dry so get some grease in the ballnut or at least bit of light lube oil on the screws.! . . . If the coupling was loose then it's 90% chance you've found your problem.

One thing I didn't like the sound of was the rattling when you grabbed the end of the ballscrew. Check if the ballscrew is floating back n forth by grabbing the end, there should be no movement.

If this is ok then I'd just grease and lube everything and put back together. If the ballscrews don't have a small flat on the end then file one on to give the grub screw a flat surface to grip on then Loctite the coupling grub screws.