Pretty sure that small movement in the prop is ok

Have you put new discs on,checked calipers aren't seized???
Check the rear of discs where they sit on the hubs,should be clean so discs sit perfectly flat

Also check the insides of alloys where they sit on hubs are clean,and wheels slide on and off hubs easily,bit of emery cloth and a smear of grease will do the trick

Anything that is connected to suspension/steering will need checking

Have you tried swapping the wheels front to back,could be a dodgy tyre