You have asked a lot of questions here that are hard to sort out without more information. With respect to unemployment, if you quit your job, you generally do not get unemployment (although there are exceptions to this rule). If, however, you have a medical condition that prevents you from returning to work, you should be entitled to unemployment. If you are denied unemployment, you have the right to multiple appeals. You also may have some rights under the FMLA, but again I cannot give you any advice on the facts as presented. I recommend you speak to an experienced employment lawyer. Many of us, myself included, will provide a free initial consultation. Good luck!
This answer is provided for informational purposes only and should not be relied on as legal advice. You should be aware that no attorney-client relationship is established through this answer and none will be established without a personal consultation and the signing of an engagement agreement.
Under FMLA, if you are eligible, you are entitled to 12 weeks of protected leave. It sounds like you were eligible since you were approved. You may extend your leave as many times as you need, up to the maximum 12 weeks in a twelve month period. In addition, your state may provide additional leave benefits beyond those under federal law.
If your FML has been exhausted, you can always contact your employer to seek additional personal leave.