No it is not. For example a meat eating human produces more CO2 per mile than a regular car. (Although most people could use the exercise so don't use that info in isolation.)
Again, many people need exercise so this might just replace that. But if you exert extra, then you need extra food. Food costs CO2, and humans are not very efficient.
Yes, that is mostly correct, but only if you are comparing products made in the same country.
A cotton sweater is cheap. But if you want to make cotton sweater in a greener process, then you need water cleaning systems, maybe different paint (which is also more expensive).
That would be counter productive. Buy local would increase your CO2 emissions. Local might have other benefits, but Co2 is not one of them.
Shipping uses FAR less Co2 than you might imagine.