L293D Voltage & Current Ratings
Yes. As you will be exceeding the absolute maximum ratings for the chip. It would not die instantly but will, eventually. If your main control signal is 12V, you can use a resistor voltage divider to feed Vi respecting the maximum rate.
Well, the best is measuring with a multimeter. Anyway, you can estimate it by looking the table at "6.5 Electrical Characteristics". It depends on the state of the pins.
It will dissipate heat efficiently as long you calculate what heat sink you must use accordingly "6.4 Thermal Information". https://en.wikipedia.org/wiki/Heat_sink#Thermal_resistance