You should leave any amounts that are "0's" on your forms as blanks in TurboTax program (unless the screen specifically tells you to enter a zero). Occasionally, there are some sections, where entering a "0" can trick the program into thinking there should be a number value associated with the box and you may get an error. Now, if the number just ends in zero like 500.00 - you can just enter 500.00 or 500 instead.
And, yes, your box 15 state would be the associated state for the local box 18-20 information.
