Your first issue is very likely Death Wobble with a good writeup on it and how to fix it in the forum's FAQ section at the top of the page. Plus there are probably at least a couple hundred posts discussing DW if you use the Search function.
The engine shutting off might be caused by a bad CPS (crankshaft position sensor). The CPS is a sensor that generates the engine's master timing signal based on pulses it generates from being mounted next to the engine's flywheel that has timing notches machined into it. When the CPS craps out, so does the engine. That's not the only possible reason of course but it'd be up on my list of possibilities.
Any Check Engine lights from when your engine died? If so, do you know how to generate the diagnostic trouble codes that would help isolate what is causing the engine to stall? If there are any diagnostic codes stored, you can see them by turning your ignition switch on-off-on three times within five seconds and then leaving it on so the diagnostics can run. Any codes it generates will be displayed in the odometer.
The diagostic procedure will always, if you do it right, generate at least the 55 code which simply says no more codes follow. A 12 and 55 code are common and the 12 only means the battery has been disconnected in past history. Codes beside 12 and 55 would likely be very useful to finding out what the problem might be.