Your asking a question that has a broad range of answers, for instance if you want to put some big oversized cd player in yes, you will need to modify the opening, however they do make cd players that will fit in your dash and have wiring harnesses to convert them to the BMW wiring. The best thing to do is ask a Stereo Shop what will fit. Cruthcfield's online has a fitment guide.
As far as your tire question, I do not know, do you have sport suspension, does it have aftermarket springs, etc? Discount Tire and The Tire Ranck can asnwer this question as well. Good luck!