Hi Dylan, you'll get more exposure if you posted this in the Mondeo sub-forum however I'll try and help as best as I can.
The symptoms you are describing sound, to me, a lot like a wheel bearing. Especially with the noise, and you mention that you can literally shake the wheel when the car is off the ground? That's classic wheel bearing play and they always do this on an MOT test to test for this problem.
What you are describing about the steering wheel shaking when braking sounds like warped discs, indeed if someone was to present that to me I would suspect warped brake discs before wheel bearings. However the only way warped discs can be checked is using a gauge which you attach and then you turn the discs measuing if they're warped by a little gauge - I can't think of the bloomin' name of the thing though
The brake disc has to move slightly to compensate for the movement of the pads on either side, at least that's what I would guess. I don't think this slight movement is anything to be concerned about.
Have you actually replaced the wheel bearing? I think it needs doing, if you can shake the wheel with your hands then imagine how much movement it has when on your vehicle at speed/braking. You need to replace that 4th nut too, are there studs or do the wheel bolts go straight through? I can't remember which setup it is on your Mondeo.
If there's studs you need to pull that stud out (use two nuts in unison), it sometimes works and I've pulled them out this way before.
Let us know how you get on, best of luck.
And if I've got some things wrong hopefully someone will be quick to correct me