You have a problem with timing.
Firstly, most non-resident taxpayers can't get an ITIN unless they file the W-7 application for ITIN at the same time as your tax return. The proof you need to send with the form will depend on your situation and is described in the instructions for the form W-7. https://www.irs.gov/uac/about-form-w7
Then, you can't get any education credits unless you have the ITIN before the tax deadline.
If you didn't have an SSN (or ITIN) by the due date of your 2016 return (including extensions), you can't claim the American opportunity credit on either your original or an amended 2016 return, even if you later get an SSN (or ITIN). Also, you can't claim this credit on your original or an amended 2016 return for a student who didn't have an SSN, ATIN, or ITIN by the due date of your return (including extensions), even if the student later gets one of those numbers.
So you will need to start by filing without the credit and with the W-7. If you get the ITIN back before the tax deadline of April 18, you can file an amended return to get the education credits. If you get the ITIN after April 18, you can still file an amended return but I don't know if you will get the credit or not. I don't know how the IRS will interpret the term "by the due date of your return (including extensions)". The due date with an extension is October 15, but you won't be applying for an extension, so I don't know if the IRS will pay the credit on the amended return if it is filed after April 18 but before October 15. Good luck.
