I'd also highly recommend checking your axles. I've seen more than a few individuals report a slight vibration that was not easy to track down, which resulted in a faulty axle. How old are yours and have you ever had them replaced? A good replacement would be GKN OEM supplier or Genuine. Don't go cheap with aftermarket axles as they can cause this issue easily.
Axles -
Mini Cooper & Cooper S (R50/R52/R53) - Axles, Bearings & Differential - Page 1
As for the click when you press the clutch down, I have seen this issue discussed mostly with 2nd gen MINI's. I doubt it has anything to do with your fluid. Maybe check the clutch arm as the 2nd gen R56 has plastic arm has a couple of gusset ribs coming out of the outer side of the arm and it can rub on some items when depressed. I have also seen individuals report that their dealer replaced a pin and adjusted the clutch pedal. Let me know what you find.