AFAIK, Ukrainian citizens follow the same rules on employment as Russians citizens - both must have a registration ("propiska") from their current place of residence even to be offered a job. The registration should state that the place of residence is in the same city as the place of employment. No discrimination here, as you see

Also, Ukrainian citizens can enter Russia with their internal passports, work there and live there indefinitely.
She should still be a citizen of Ukraine because she was the citizen of the USSR and resided in Ukrainian republic on 24 August 1991... unless her parents left Ukraine as refugees and renounced Ukrainian citizenship at the point of exit. During Soviet Union it would be the case, but currently Ukraine does not revoke citizenship from leaving refugees. I am not sure how the situation was in 1992.