What kind of oath did she swear, and what is the ruling on possessing this piece of land from the state after falsifying information?

Swearing falsely is a "Yamin Ghamus" (a perjurious oath) that immerses its taker in sin. The matter worsens if it leads to unlawfully consuming wealth and encroaching upon rights, such as seizing land without entitlement. The one who commits this must engage in sincere repentance and return the land they are not entitled to, as the condition for owning it has not been met.