I am not sure you want to be a Foreign Illinios corporation! When you register as a corporation in State of Nevada, and you are conducting business in State of Illinios, then you have to obtain permission to do business in Illinois, furthermore, there is a annual filing fee payable to State of Illinois, and then you have to obtain a certificate in good standing from State of Nevada, which again will cost you more money and time.
At the end of the day, it probably makes more sense to incorporate in State of Illinois in my humble opinion.
As far as deductibility of expenses incurred in Illinois, you can do that regardless of where you incorporate.
I currently have a client based in NJ doing business in Illinios,and so I am talking from experience! The process is a little tedious and it does cost a little money excluding my fees!
So, in the end please seek professional advice prior to incorporating in Nevada, because at the end of the day, you still have to pay federal taxes on profits from Nevada and you will be subject to Illinois minimum S Corporation taxes and furthermore, you will have to deal with the hassle of a lot of additional paperwork, time and fees incurred for a foreign corporation.