First, please note that unless the Police witnessed the accident, the Police Report does not come into evidence. With that said, if you have a stop sign, you are supposed to wait until the intersection is clear before you proceed. The other driver hit you in the rear quarter panel, which means you were "almost" through the intersection when he hit you. Accordingly, its entirely possible that liability will be split between the two of you if the case was ever tried.
You are not responsible for pre-marital debts, but if you put money into a joint account, or buy a home together and both are in the deed, joint assets can be seized to satisfy the debt. While you may still be able to show that part of the money in the joint accounts is actually yours, it is a complicated procedure, and your assets will be "detained".
You can definitely sue. Whether the case is worth bringing over less than two month delay in treatment is unlikely. Will you be able to find an attorney to take your case - not one that understands the costs of bringing a malpractice action against a hospital.
From the day you sign the release, and return it to the lawyer, it should be around 30 days, depending on how the defendant cuts the check. The check may need to be signed by you, prior to being deposited, and then it has to clear escrow. There are situations where it can take much longer. For example if the defendant was a municipality it can take 3 to 4 months. If you are concerned about the time its taking call your attorney.
There are fractured ankles, an then there are fractured ankles, and without more, no one can answer the question. Hopefully, your heal completely and have minimal residual injuries. You need to consult with a workers compensation attorney as soon as you are able. You also may want to speak with a personal injury attorney to see if there are any other avenues for you to pursue other than workers compensation.
Your post is unclear, and I suggest that in the future, when you need something from a Court, and English is not your first language, that you consider hiring an attorney. The one part of your question that is clear, is where you ask if you can get your money back from Appellate Court that heard your appeal. You have zero chance of getting your money. None, whatsoever. The money you pay is for processing, not for a favorable result.
You should have a copy with all signatures. Also, if you don't want the attorney to call the executor, you tell the attorney Don't call the executor, and he should honor your wishes. The attorney is your attorney with respect to this matter, not the executors.