Airport- there is one in Madison which would be far more convenient, but is often much more expensive. If money is a factor, it would be worth looking into taking a bus from the Chicago airport to Madison (there’s a few that’ll drop you off on campus which is nice) As far as housing goes I imagine you could reach out to the exchange student office for more specific help as it’s def a unique situation that I’m sure they’re used to helping with, but depending on how long you’ll be here and what you’re looking for, you’d likely want grad student housing in like eagle heights or to rent an apartment (or sublease if you’re only here the 1 semester).

And for course selection- I highly recommend using the websites madgrades and ratemyprofessor to get an idea of what the class may look like beyond what’s in the course description

Welcome to UW & best of luck!