It could be anywhere from 82R to 680R, with no other data it's hard to tell. If the resistor is burned, the transistor base is likely open. Check the 240R resistor, it dissipates more than a watt and may be damaged as well.
Not really, it ensures the output transistor stays turned OFF if there is slight leakage in the driver transistor - it's good practice to include it, but it's value can be almost anything higher than the lower resistor - preferably a LOT higher though.
Quick thought - if that resistor has burnt up, it can only happen if the output transistor has failed (O/C BE), otherwise there's only 0.7V across it.
Not really, it ensures the output transistor stays turned OFF if there is slight leakage in the driver transistor - it's good practice to include it, but it's value can be almost anything higher than the lower resistor - preferably a LOT higher though.