Is it permissible for a Muslim to pray in a car without Wudu or Tayammum ("Salat Faqid al-Tahoorain" - prayer of one who lacks both means of purification), knowing that the time for Fajr prayer might expire if he waits until arrival?

It is not permissible to perform the obligatory prayer in a car except out of necessity. Therefore, one must disembark to perform it on the ground. If the car starts moving after the prayer time has begun, the prayer should be performed before it moves. If it starts moving before the prayer time begins, and the worshipper knows they will arrive before the prayer time ends, they should delay the prayer to perform it with all conditions met. If they do not pray until after the prayer time has ended, and the entire prayer time is spent traveling, then it is obligatory to stop the car for prayer. If that is not possible, the prayer should be performed according to the prevailing circumstances, with re-performance required by some scholars. If you have ablution, pray with your ablution; otherwise, perform tayammum. If you cannot find anything for tayammum, then pray according to your circumstances.