(The plane [from Mexico to the UK] may go over US Airspace, however, I don't know the flightpath)
This is irrelevant: you don't need a visa or any other documentation to fly over a country without landing. If there was an emergency and your plane had to land, they'll save your life first and make arrangements to deal with any immigration issues second.
Am I transitting?
No. Transit means entering a country for the sole purpose of getting to another country, e.g., by taking a connecting flight. Your purpose for entering the US is to be a tourist there and, when you've finished doing that, you're going to go be a tourist in Mexico.
Am I staying in the US?
Do I need to provide onward documentation?
You need to convince the immigration officer that you'll leave the US. It's a good idea to have a print-out of your itinerary but you might not be asked for it. I reckon I've been asked about 10-20% of the times that I've flown to the US; actually, one time I didn't have a print-out so I fired up my laptop and showed them the actual email. The thing about onward travel is that anyone could buy a return ticket and not show up for the return flight so the fact that you have onward travel doesn't actually prove much to the immigration officer.