On the pressure issue, I'm not sure what the actual pressures should be but it will tell you in your hand-books, "the tyre pressure management thingy" as you put it

, is better at picking up a sudden loss of pressure, a slow puncture / loss of pressure is not always detected as easy (all tyres will lose some pressure over time), so your best checking what pressures your MINI should have and also check the pressures from time to time manually, and remember to reset the system if the pressures have been altered

, there are threads on here on how to reset the system or again, read your hand-books.