Is it permissible to invest deposited funds in purchasing land while there is a debt owed to the state, being paid monthly, knowing that repentance has occurred and a portion of the money has been returned to the state through a charitable committee?

One must take the initiative to rid oneself of ill-gotten wealth, and postponing it, while being able to dispose of it immediately, is not permissible. If the saved money is not enough to repay all of it, then pay what is available and pay the rest in installments according to your ability.