[msej449]

1) If my rolling diameter is almost identical (24.72 fronts, 24.75 rears). Does this count as a square setup? Although, the sidewalls will obviously be different (12% increase in the fronts)

'Square' tends to mean that all dimensions are the same on all four wheels. So by common definition, no.

2) Is running a setup like that optimal? Are there downsides? Aside from rotating tires etc. If it is not, What is the optimal way to run a "double staggered" setup?

Probably not. Probably yes. What you describe may not be very desirable in terms of handling. 17"x8" fronts and 18"x9" rears are definitely not a combination ever tested by BMW, let alone approved for this model, or any of its mainstream cars. [edit: apparently not - see below]And I'm fairly sure that the feedback on here would be that this would be a very unusual and possibly dangerous setup. Or at a minimum, would produce some very unusual driving dynamics.

3) Does the sidewall height difference matters ?

Yes, significantly. All other things being equal, the lower the sidewall height, the easier the wheel is to turn but there's a price to pay - this is a zero sum game: a lower sidewall i. gives a harsher ride, ii. is less resistant to hyroplaning and iii. is more prone to pothole damage. You need to be aware of this if you swap to wider wheels/tires with narrower sidewalls (i.e. low-profile). Obviously, if you live in a low-rainfall area with good roads then you may be very happy with the result. But if you live in an area of higher rainfall with poor road surfaces you may not.

I also wonder how an insurer would treat a serious accident claim if a post-accident inspection revealed such an unusual, if not unique wheel setup. It's not like fitting a slightly wider tire, or a slightly oversized wheel with spacers. If they asked BMW, I'm fairly sure they'd be pretty negative about this as being a long way away from anything standard, to the extent of being gratuitously dangerous. Which might not bode well in terms of your liability. Sorry to sound negative, but I think that on handling dynamics alone the 17/18 setup is at best questionable, even before any of the legal issues come into the frame.

But other 2addicts may have different advice - I'd happily defer to their expertise. This is just one person's view.