What are Food miles?
Food miles is a term which refers to the distance food travels from the time of its production until it reaches the consumer or end-user. .
What is a carbon footprint?
A Carbon Footprint is a "measure of the impact human activities have on the environment in terms of the amount of green house gases produced, measured in units of carbon dioxide"[1] It is meant to be useful for individuals and organizations to conceptualize their personal (or organizational) impact in contributing to global warming. A conceptual tool in response to carbon footprints are carbon offsets, or the mitigation of carbon emissions through the development of alternative projects such as solar or wind energy or reforestation. A carbon footprint can be seen as a subset of earlier uses of the concept of ecological footprints.
Is climate change a fact
No it's a theory which is overwhelmingly supportted by a huge body of evidence. The IPCC states that 90-95% is likely to have been in part caused by human action. 
Can I make a change?
Yes eat less just kidding, food makes up about 2 tonnes of CO2 per person. You can make an effort to cut your carbon footprint from food by buying locally, which reduces your food miles. A quarter of the trucks on our roads are carrying food and raw materials for the food industry. Yet many of the biggest energy inputs (and hence carbon outputs) of our food come from growing and processing food, rather than transporting it. Manufacturing fertiliser, heating greenhouses and food processing are major energy guzzlers, so buying locally is by no means automatically the greenest option. Trucking in tomatoes from sunny Spain often uses less energy than heating a greenhouse in Ireland, for instance.
[1] http://www.carbonfootprint.com/