What is the blood money (diyah) for physical injuries (fractures and wounds) and material damages (to the motorcycle) resulting from a traffic accident caused by a car that hit a motorcycle? And is taking this blood money forbidden (haram)?

If the car owner is at fault, he bears the damage you incurred. The assessment of the damage is referred to the Sharia (definition) courts or their representatives, which is known as "hukumat al-adl" (just compensation). The jurists have stipulated the necessity of just compensation for every offense that does not have a specific prescribed legal estimation. It is permissible to reconcile for a specific amount regarding the offense. There is no blame upon you for accepting compensation if it is assessed on the offender or from an insurance company.