Ivan's coupe: seeing RED

[Ivan141]

Guys, need some help....
My car is going for it's APK (MOT) this friday, and I have something that is bugging me.

I started to notice a slight rumbling noise from my left rear wheel in corners to the right. I thought a bearing had gone bad so I took the half-axle in question out (this one is so loose i can pull it by hand) for inspection.
On closer look the bearing feels good as new, but the whole half-axle can move in and out half a millimeter when mounted.
I couldnt get the bearing to move when it was out of the car though.
What can be causing this? maybe the retainer moved a bit?

Also my right rear brake caliper is bad... it always sticka a little and the piston is really hard to turn back in...anyone have a spare somewhere?
This one has been like this since I bought the car so it's not bad enough to fail APK, but still...would like to fix it.