Illinois permanent Resident but do on-site contract work in Iowa. Employer (in Michigan) withholds Illinois taxes

I work an indefinite contract assignment in Iowa where I work on-site.  While I rent an apartment in Iowa, I still get my bills, voter registration, driver's license, car insurance, doctor, etc.  all remain in Illinois.   My employment agency with the contract (in Michigan) withholds Illinois taxes.  Illinois.

 

1-A. Illinois and Iowa have a reciprocity agreement.  Do I have to file taxes in both Iowa and Illinois?

1-B. Do I file as a resident in Illinois (where my permanent residence is and where my withholding was sent)  and a non-resident in Iowa or do I file as a Iowa resident and then a non-resident return for Illinois?

1-C.  Do I even have to file a non-resident return in either state?

 

2.  I have a primary car in Illinois, but bought a second car in Iowa for use when I am on-site there. I paid $2399 in sales taxes for this second car for use in Iowa.  Can I deduct the state sales tax in either state?