An F-1 student is considered a non-resident alien (NRA). As an NRA, you have two choices.
1. You file married filing separately, only reporting your own income and deductions. She files a 1040-NR for any income she has (turbotax does not include this form, you have to go elsewhere).
2. You make an election (choice) to treat her as a US person for taxes. You can file a joint return but you must report all your combined income.
The designation "valid only with DHS authorization" is different than "not valid for employment." You would answer that her SSN IS valid for employment, assuming she is only doing work as authorized by DHS. For an F-1 visa, that usually means work connected with her schooling. She would not be valid to have a side job for extra money unless that was specifically authorized.
