Hi - Only just got this tablet, so have a few questions:
1) Is it supposed to come with a USB cable?
Yes. It comes with a normal USB to USB cable, both ends male (like on the end of your mouse)
2) If so, where is the cheapest place to pick one up from?
Dunno, your local pound shop? Fabricate one yourself from 2 unused USB things, cross the wires. (You've got 4 wires, just cross 1 with 4, and 2 with 3)
3) Is using a USB cable the only way to reset the tablet?
If you haven't installed Clockworkmod on it, then yes
4) The touchscreen has stopped working (I think the kids may have re-calibrated it) What is the best way to fix?
Reinstall a new rom
For reinstalling a new ROM, surely for the first time, you need to get into NVflash mode, that is a bit tricky to get there as it requires a sequence of buttons in the right timing, be sure to do this while it's connected to the wall socket, or otherwise it won't work as well. Read yourself in about the Vega, and the current stable and latest rom must be VegaBean, however I did not get that from XDA but from some other forum.
For getting the hang of NVflash the first time, keep a beer at hand. It tends to freak people out when it doesn't work first time.
Btw, I'm wondering why you just got this tablet, I have one as well for almost 2 years now, but the unresponsive touchscreen and low quality of it bugs me as hell in this day of age, going to buy a Nexus 7 as soon as it's in stock again. Hope you will be happy with it though.