The first thing you likely should practice is locking your doors. If your door was locked, the neighbor likely would not have been able to come in to your place. With the recent newspaper headlines about burglars coming into houses whose doors were unlocked, you should be concerned about your safety.
If you want criminal law charges filed against the neighbor, you will need to make a report to the police. The police may investigate. If the police thinks there is a winnable case, the police will file a report with the prosecutor. If the prosecutor thinks there is a winnable case, the prosecutor files criminal law charges against the neighbor.
Frankly, given that no threats were made and no one was physically injured, the police likely would do nothing more than take a report. The police may even decline to take a report. If you had called the police right when the neighbor was in your home, the police may have done more for you.
If you report the incident to your apartment manager, you may get more results, especially if the neighbor has a history with the apartment manager.
Quiet hours do not actually begin "after 10 PM". If you were playing music loud enough, you can be found to have violated the city's noise ordinance any time of the day. In Seattle, the noise ordinance is mostly in Chapter 25.08 (NOISE CONTROL) at http://clerk.ci.seattle.wa.us/~public/toc/25-08.htm .
Probably not. You need to contact the police first. Try to reach out to her in a civil manner first and see if you can get her to not enter your apartment without permission. If that does not work, you have the option of getting a personal restraining order. You would need to check with the Seattle district court.
The advice given is general for information purposes only and should not be relied on. You should consult with an attorney of your choice to fully advise you about your legal rights and obligations.