an MOT isn't a guarantee your car is safe, it should be but it isn't. The tester may have missed something.
The creaking at full lock is most likely to be the strut top bearings - this probably isn't what's causing your steering problems.
The violent shaking and the steering wheel off centre would suggest a worn track rod, could be inner or outer. this would also give you the vagueness in your steering.
Assuming your wheels are balanced too? Does the symptoms change if you swap the front and rear wheels?
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The rain kept a trollin'
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