Number one is caused because when the exhaust is cold, it is retracted and possibly touching the rear valance which causes the resonance/buzzing you hear. If the 'rattling' is pretty severe, then it sound's like one of the silencers or most likely the manifold pre-cat has burnt out. What happens is the glass fibre sound deadening in the silencer can heat up so much that it melts and forms little glass 'balls.' This then rattles when you are setting off from a standstill/manouvering etc. The car only has 400 miles. I know, but it could be a manfacturing defect...If it goes away from some driving (i.e. allowed to warm up) and doesn't resurface again, then most likely it is scenario one.
Number 3, a loud ticking, sounds more like a tensioner or idler pulley issue than a crank pulley issue. A number of things can cause this sound, most fixes come from repacing the supercharger, the idler or tensioner assembly. That's all that can cause a ticking sound from the drive belt area of things. If the ticking is not that noticeable, then it could be just your tappets in the head at work. I remember mine being faintly 'tickkety' even when standard. A thicker oil (15W50) helped eliminate alot of the engine's natural noises.
Number 5, this sounds like a flywheel issue or a faulty throwout bearing on the clutch if you are having problems with engaging the clutch at all. If there is a little 'resistance' or 'notchiness' to the clutch's engagement, then that can be rectified by replacing the clutch slave cylinder.
Alternatively, if other 05 owners are getting the same sound, it could be down to the new LSD. My car makes all sorts of tapping sounds at idle with the gear in neutral, but then again I have a lightned flywheel with no dampner and a Quaife LSD, so no wonder
Hope you get things sorted soon.
Cheers,
Henry
p.s. Minis are never perfect unfortunately. They all have quirks. If this is a real issue, then I can recommend Lexus. These are by far the best engineered cars on earth right now bar none. Even the Maybach gets run close for build integrity, and that does cost the earth!