Answers:
Either there's some debris in the cold water pipe work stopping cold water entering the tap or there's a valve for cold water turned off leading to the tap. if that's all fine then possibly would be a new tap. craig clw plumbing pontefract.
To move a radiator it would depend how much pipe work is involved but as you say a couple feet that should be be too much unless you want the pipe work hiding under floor boards which is extra work but i would charge between £80-£100. craig clw plumbing pontefract.
The combi-boiler hot water production flow rate and incoming mains pressure will ultimately give you your final outlet flow to any shower mixer. of the two choices of manufacturer i would plumb for the aqualisa although mira are just as good
It could be a rubber washer what's in the gland of the tap what has warn down and could possibly just need a new rubber washer if that's not the problem then could mean a new tap but to change the washer you would need to isolate your water and take the head off the tap and unscrew the tap fitting from the tap where you will then see the washer what would need changing.
I would say a call out charge should be made anytime after 6pm of £20 i would not charge one through daily working hours unless it was a distance and then i would only charge fuel costs. craig clw plumbing pontefract