I do not see any problems. The green card allows her to work legally.
This is not legal advice and a client attorney relationship is not created.
Yes, absolutely. Since she is a green card holder there are no restrictions on her employment whatsoever. That inscription on her SSA card is a remnant of the days before she obtained her green card and should be ignored.
Kindly be advised that the answer above is only general in nature cannot be construed as legal advice, given that not enough facts are known. It is your responsibility to retain a lawyer to analyze the facts specific to your particular situation in order to give you specific advice. Specific answers will require cognizance of all pertinent facts about your case. Any answers offered on Avvo are of a general nature only, and are not meant to create an attorney-client relationship.