More complete combustion would result in more CO2, H2O, and energy. The by products from incomplete combustion are the ones we want to limit - CO, C, various N and S compounds etc.
Not always. Nitrogen oxides are due to higher temps which is more efficient. In order to meet emissions standards, you often take a hit in efficiency (or at least drive-ability).
Makes sense - it's not incomplete combustion but rather atmospheric contamination that allows for NOx products, and the amount of those is dependent on heat of combustion. Thanks!