Is red wire the positive wire?

Answer 1

Yes

CaveatIn general, when working with DC, the red wire is positive and the black wire is negative.

In the US and Canada, when working with AC, the colored wires (red, black...) are "hot", the white wire is neutral and the green or bare wire is ground.

Note that the above is NOT a requirement for "switch legs".

Answer 2

Yes, it is generally safe to assume that the red wire is positive. If you're not sure, you can always check using a multimeter set to AC or DC (Whatever the circuit is outputting). Attach the positive lead to one wire and the negative to the other, if your multimeter reads negative voltage, then the wire you have the negative lead on is positive. But before testing, ensure that your multimeter is rated to handle the voltage from your circuit otherwise you may destroy the meter.