RT's responses are on target. To address your specific questions:
Yes, though it will be an expensive repair. Probably in the $500 to $1000 range.
If you cannot get to a Toyota dealer for the coolant and the cap then, at a minimum, you need to get some distilled water from any grocery store. I would worry about the overnight temps in SD at this time of year. You can pick up a cap at most any auto parts store.
Yes, there is a problem with driving it with any cooling system failure. A 400 mile trip is out of the question until the issue is fixed. You will most likely ruin a very expensive engine.
As RT mentioned, it might be as simple as a radiator cap that is not holding pressure; therefore "boiling" out your coolant. On the other side of the spectrum is the failed HG which is a serious problem and an expensive fix if you take it to a repair shop. The loss of coolant could be from a number of different things between those 2 ends of the spectrum.... thermostat gasket, radiator hose, heater hose, leaking freeze plug, leaking radiator, leaking heater core, cracked engine block, etc....
The first thing you have to do is determine the cause of the coolant loss, then go from there. Post back what you find and we will be happy to help.
-B-