Some questions about current and reading electrical characteristics from a datasheet
The input currents tell you what the chip will require from the device that's driving it. i.e., your micro-controller.
The logic supply current is what is required to run the logic in the chip. The datasheet shows some of the internal transistors, etc.
The high impedance refers to the ability to disable the outputs: neither the pull-up transistor is on nor the pull-down transistor so the output effectively isn't connected to anything and appears as a high impedance or high resistance - effectively an open-circuit.




Figure 1. Logic supply (1) and motor supply (2).

The datasheet says:


  A VCC1 terminal, separate from VCC2, is provided for the logic inputs to minimize device power dissipation.


As is good practice on many motor systems a separate supply is used for the logic and motors. The 35 mA refers to Vcc1. You can pull up to 1 A continuously on Vcc2, if I read the datasheet correctly.