Unleaded - any octane.
[EDIT] The Mini Cooper S (ie supercharged version) suggests Premium (91 octane) but this is a highly debated point on the internet. After much reading the general consensus was to run at least 2 tanks of regular and note your mileage, then step up to the next level of octane and do the same thing. Keep increasing fuel grades until your mileage stops improving. Note that when doing this you should try to keep your driving style constant (both speed wise and highway/city amounts). Personally I'm playing it safe and sticking with premium.
unleaded
Premium gas
Use exactly what the manufacture recommends and nothing else.
Regular gas should be fine
If it is a CVT transmission then yes you can use cvt gearbox oil in a mini cooper.
The 2008 MINI Cooper runs on premium unleaded (required).
The 2002 MINI Cooper runs on premium unleaded (required).
The 2007 MINI Cooper runs on premium unleaded (required).
The 2012 MINI Cooper runs on premium unleaded (required).
The 2004 MINI Cooper runs on premium unleaded (required).
The 2005 MINI Cooper runs on premium unleaded (required).
The 2003 MINI Cooper runs on premium unleaded (required).