Answer:

2. What are check digits good for? Why do they bother to put check digits on UPC codes and things like that? (answer)

The check digit makes it possible for a computer to quickly verify whether a code has been entered properly. It's easy to make small errors in reading in a code (like entering one digit incorrectly, or switching the order of two digits that are right next to each other), and the check digit makes it possible to catch almost all of those kinds of errors, so that the code can be re-entered correctly (instead of it just showing up on the computer or cash register as the wrong item). It means that if a bar code is scanned and entered wrong at the register, the machine beeps to say "fix the code" instead of just accepting the wrong code and charging you for the wrong item.