Changed my tyres yesterday and notcied the rear pads were looking pretty nailed so thought I'd change them (£16 from Hein gericke so not bad

Having put the caliper and pads back together it doesn't seem quite right.

If I spin the rear wheel it spins but then gets to a sticky part as if the wheel wasn't straight or the disc was warped, and stops. I can move it on by hand but a little effort is needed.
The rear caliper seems to move a bit side to side with the wheel turning - assume this is part of the same issue??? Ran the engine on a paddock stand and you can really see if moving - its only about 3mm movement.
I have checked that the chain adjusters are in the same place and it looks straight?
The rear brake works but has a lot of traval at the mo - could just be down to thickness of new pads?
THe old pads I took out were Nissin pads (originals?) and seemed to have a backing plate fit onto them - should I have reused the backing plates?
Could it just be:
a. wheel isn't straight?
b. new pads not put in properly?
c. Not put caliper back on properly?
d. just needs time to settle in - take it for a test ride and see?
e. something else?
I will prob go for a little bimble today and see if it settles in.
Worrying me a bit as I need to get this sorted by end of April as I am going to the nurburing where confidence in brakes is always a good thing.
Grateful for any help...
Adam