Runflats are definitely expensive and hard-riding. They will get you 50'sh miles down the road in the event that they lose air due to a hazard, since there's no spare tire. But most find that substituting "normal" tires (and adopting some type of flat-tire incident measures) are a great improvement.
The sport button changes the MINI's electronic controls to quicken the throttle response, and to stiffen the steering. In using mine on my 2012 MCS
, I've not noticed any changes in fuel consumption, particularly.