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.