The original design did not have a 'track' along the full route. Cars would more or less hop between different sections. On Mars that represents clear reliability issues, but the ability to avoid building load barring bridges over gorges could be a major cost savings.
Sure, but I think it's fair to call a train that is powered with electromagnetic pulses from stationary coils something different than a train that is powered by an onboard engine.
Yes, although I think maglev trains use continuous linear motors while if I understood the original proposal correctly, the hyperloop would be more like a series of railguns evenly spaced along the route.