Question 2 is easy.
http://www.gridwatch.templar.co.uk
Gives you national grid statistics including national frequency at about 5 minute intervals.
Question 1 depends on machining accuracy, particularly of the step-'pulley' which is likely a diecasting in a BSR and liable to some shrinkage.
Question 3, I haven't a clue. It could be quite good - crystal controlled, but there may be software fudges galore.
Is it a real synchronous motor or just an induction job with uncertain slippage?
You could print a stroboscope and use a neon bulb. The mains is fairly accurate. For timekeeping, the number of cycles/day is controlled.
Shorter term, the frequency is varied, low to demand extra generating capacity comes on-line, high to shed capacity.
David