Try this site for measurements and a simple visual difference. Since your change is more extreme it might be harder to know if everything will clear. Maybe entering a factory 17" option for your car as the before will give you some better info.
http://www.willtheyfit.com
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The F56's come with 205/45's so I would think you'll have plenty of space for those to fit.
Offset isn't a drastic change, and 17x8 while being slightly wider, will be covered with that size tire.
The spedo may not read correctly, but does anyone have a MINI that does? LOL -
Not one of the 4 MINIs I've owned the speedo has been off -