If the owner of the car is in the occupied territory, it will be almost impossible to re-register the car. You can try through Diya. Re-registering a car by proxy does not give you ownership of it, but, in fact, gives you the right to use it.
To receive a deferral based on health status - you need to pass the VLK and receive a VLK resolution on temporary incapacity.
"Excluded from military registration" means that a person loses the status of a person liable for military service and is not subject to military registration obligations. In particular, such a person cannot be called up during mobilization, after exclusion from registration, he is not obliged to undergo a military service examination, update his registration data, such a person cannot be served with a summons. This concept is permanent and the person should not re-register.
Check the information through Reserve+. You should create an electronic military registration document and analyze the information it contains. If it turns out that information about exclusion from registration is missing from the electronic military registration document, apply to the CCC in which you are on military registration according to the registry data. In the application, you should ask to enter information about your exclusion from military registration based on a military ID card or other document containing such information. This can be done by visiting the CCC in person or by sending an application through Ukrposhta. It is better to send the application with a description of the attachment. If such an appeal to the CCC does not lead to the desired result, you will have to act through the court by filing a lawsuit for the obligation of the CCC to enter information into the Unified Register of Conscripts, Military Obligees and Reservists regarding recognition as unfit for military service with exclusion from military registration, in accordance with the information specified in the military ID card or other document.
It is very important not to agree to retake the VLK if you have already been declared unfit with exclusion from military registration. Such exclusion is irreversible and you do not need to retake any medical commissions.