You can sue your employer once the EEOC gives you a right to sue - or your attorney can request it after 6 months. Constructive discharge is a high standard to meet but youy may have it. You have a lot of moving parts here and need an experienced employment lawyer to guide yo through.
Sounds like retaliation to me. The damages for which could be a lot. See the state agencies again and add the retaliation to your complaints. Retain counsel
The above is not intended as legal advice. The response does not constitute the creation of an attorney client relationship as this forum does not provide for a confidential communication.
You have several good theories here for an experienced employment lawyer to get a good result for you. However, "lying to unemployment" is not a lawsuit and is not grounds for recovery. Sometimes I find my clients focus on things that really upset them but are not causes of action. Your only real bet for relief on an unemployment claim is through the unemployment system, so you should appeal the denial.