Fiance visa but you must be a USC to do so.

Work authorization will likely take 4-6 months post submission.

No not for renewal but for initial application.

No the I864 is not required at this initial stage.

Yes the A number or certificate number can be used rather than certificate in certain instances.

Yes employment based visas are a possibility but she must be eligible to do so. Consult with an attorney for guidance.

He can still independently obtain tourist visa if eligible.

Very difficult to provide estimate but check with the consulate for guidance.

Appears this notice was sent in error.

Yes this should not be a problem but you can check with the school.