Am I permitted to receive financial compensation from the car driver, knowing that I believe I am at fault, while others testify that the driver is at fault, and I have already filed a lawsuit seeking compensation?

Determining who is at fault in traffic accidents falls to the competent authorities. Whoever the authorities rule to be at fault is obligated to compensate for the damage he caused. The determination of compensation is up to the Sharia courts, unless the offense is one for which the Sharia has specified a fixed blood money (Diyah).