To see if you have an alarm, look on the left hand side indicator stalk - does it have a red tip? If so you have the alarm, if not you don't. You should also have a motion sensor above the rear seats.
I find that locking your car with the windows down allows wind to blow through and in turn set the alarm off. I found this out by accident, and the alarm is bloody loud!
No MINI's come with a spare tyre as standard, although there was an option to spec a space saver spare, but I don't know where its kept if you have it, sorry. You will just have to rely on the runflats, I have had to drive on a flat on more than one occasion, and I can assure you they do their job well.
Hope this helps.
