Specialized Rockhopper Comp

Hi all,
I have two niggling issues on my rockhopper that I hope someone can jump in on and give some advice.
The first issue is the forks always pull to the left under heavy braking or letting go of the bars or just pushing the bike. Think this could possibly be too much preload on the headset? Or could anything else cause this?
The second I have noticed for some time, the rear vibrates or judders in wet and dry under medium to hard braking. I have changed rotors, pads, tightened the rear caliper, made sure it is aligned etc, what more could I be missing out on? No cracks to the frame of fractures.
Her in question

Any ideas, think the first will be easy to solve, but can't quite hit the nail on the head with the rear end.
Picture is outdated, have a deore XT rear brake with matching ICEtech rotor and front brake hose in correct routing. And all cables shortened and tidied up.
I have two niggling issues on my rockhopper that I hope someone can jump in on and give some advice.
The first issue is the forks always pull to the left under heavy braking or letting go of the bars or just pushing the bike. Think this could possibly be too much preload on the headset? Or could anything else cause this?
The second I have noticed for some time, the rear vibrates or judders in wet and dry under medium to hard braking. I have changed rotors, pads, tightened the rear caliper, made sure it is aligned etc, what more could I be missing out on? No cracks to the frame of fractures.
Her in question

Any ideas, think the first will be easy to solve, but can't quite hit the nail on the head with the rear end.
Picture is outdated, have a deore XT rear brake with matching ICEtech rotor and front brake hose in correct routing. And all cables shortened and tidied up.
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There is no secret ingredient - Kung Fu Panda
London Calling on Facebook
Parktools
This could make it pull to the left and are those superstar wheels you have on the bike.
the rear brake as long as its not squealing or making loud noise i would leave it alone, you could clean the rotor with isopropyl alcohol and see if that helps.
Don't really want to put IPA on the rear rotor as don't want to bed it in again, but no contaminants are on the rotor, the rear brake stops me, just annoying how I can feel the frame vibrate when using the rear, and its quite a big vibration almost like something is causing a resonant frequency.
Doubt it would be hub bearings either as the rims are only 2 months old and yeah they are superstars.
Think the headset I can sort by just servicing it, but the rear I am out of ideas on.
can you elaborate?
The headset will not impart a rotation if it is worn, it will just feel rough to turn, changing the headset will not fix this unless you have a mass of play in it, in which case sort the preload!
Thanks for that rookie. I can see where you are coming from.
But I can confidently say the bike has never been dropped nor the forks twanged or anything like that. Had a good rock on the suspension and no play in the bushings either.
Taken on board about how a headset can't cause it. So just loosened the headset and stem and reset it all, so will see how I get on, on the commute. Thinking back, it started from when I last stripped it all down, so unless I didn't do something right with the headset I don't know.
Any ideas on the rear brake? It is a very loud dull type squeal with lots of vibration.
Put an old brake on, to try and see if it is in the frame or brakes. Will post a vid if it helps
Rear brakes could be a contaminated disc, give it a clean with IPA.
Just undone preload and stem and made sure everything was seated properly, tightened back up last night. On the commute today perfect not wanting to go to one side.
Reluctant to IPA the rotor, but will give it a try. And will chuck some copper grease on back of the pads, will update tomorrow when I'm back.
There is no secret ingredient - Kung Fu Panda
London Calling on Facebook
Parktools
Or are metallic pads porous
Why would you be reluctant to clean the disc??????
There is no secret ingredient - Kung Fu Panda
London Calling on Facebook
Parktools
Because they think they might remove the bedded in pad material off the disc ?
There is no secret ingredient - Kung Fu Panda
London Calling on Facebook
Parktools