If you want to move out you will have to give written notice. If you have a lease, that will be binding until it terminates, A dirty house, ants, mosquitoes and a leaky sink are not sufficient reasons to break a lease.
But 'unlawful detainer' means you are being evicted for non payment of rent. If you are living there and have not been paying, you will lose the action your landlord is bringing.
Can you move? Yes you can move. You will still owe arrears but there will be no eviction if you have left before the case is heard. This debt will be on your record however.
Can you sue her? For what would you sue. A dirty house is your fault. Ants and mosquitoes are annoying but harmless. She will say that she is attempting to get the leaky sink repaired. It costs money to sue someone. On the basis of the facts you have given, you will not win. If, in addition, you have rent arrears judge may make you pay her legal fees as well as your own for wasting the court's time.