All your questions is answered in the datasheet, bur may need some decoding.
From the datasheet you will find that the drivers need at least 2.4V input voltage to turn on full. The 350mA is the max current for each output, BUT you can't drive all outputs at the same time. From the graphs at page 2, 5 and 6, you will see that the max power dissipation is about 1.5W as best case with 25 deg ambient temperature.
This will result in a possible continuous current for all outputs at the same time to about 100mA. This will be close to the limits for the chip. Reducing the number of active outputs, and/ or duty cycle will increase the possible output current up to max 350mA per channel.
If you design for long life of operation, it is normal to be a bit conservative when loading the chip. You should also take ambient temperature into consideration.