Magnetic trainer failure
Let's start with some quick maths. I'm guessing the roller has a diameter of 40mm based on the picture. Since it's in contact with the tyre, whatever speed your speedo reads is how fast that roller is going. But it's 40mm in diameter. So, at 72kph / 45mph we have:

Speed = 72kph = 20m/s
Diameter = 40mm = 0.04m
Circumference = π d = 0.125m
Revs per second = 20 / 0.125 = 160 Hz (9500 rpm)


The magnetic rotor is bigger, perhaps 100mm diameter, and we want the centripetal acceleration:

a =  v² / r
  = 20² / 0.05 = 800 m/s² (about 80G!)


Note that that scales with the square of the speed. So at 108kph / 70mph you're going 50% faster but the force on the outside of the rotor is 2.25 times bigger (about 180G).

1. In what ways do magnetic trainers commonly fail?


The one you care about is overspeed. Either explosion due to too much centripetal acceleration, or an imbalance causing the shaft or mount to break. It looks as though your one failed that way, either through the trainer being knocked at some point or being slightly out of balance when it was made. I've also seen bearings fail through overheating, although that shouldn't happen now because bearings are so much better.

2. Was there anything I was doing wrong that caused the failure? 


Possibly going too fast, possibly going too far. If the flywheel was slightly out of balance it would probably fail eventually regardless of how slowly you went, but if you look at the centripetal acceleration, since that depends on the square of the velocity so does the "wear" caused by being out of balance.

3.  Are newer trainers designed better and/or can they accommodate a greater speed? 


Possibly, and I would hope so. It's been a few years since I broke one, but I've never been a world class cyclist and I have broken two different trainers simply by putting too much power into them (one admittedly at about 1300W). The problem is, to some extent, intractable. People want cheap, light, quiet trainers, but those trainers have to somehow get rid of 500W or more of power for as long as you care to sit on them. Doing that in a light, quiet, cheap container is hard.

4. Would another type of trainer (fluid, wind, etc) failed like this?


Probably. If you bought one with a bigger fan or other dump zone, no. But that would mean the old school "bike wheel with fan blades riveted on" that people hate so much. One alternative that would work is the "pedal powered generator" setup that the green kids are so fond of building, because they usually have bigger flywheels that consequently rotate more slowly (and as I keep saying, the problems go up with the square of the speed, so twice the roller diameter means 1/4 the force). But they're big, heavy and expensive compared to a trainer, and you have to build your own if you want that power output (commercial ones seem to top out at about 200W - I keep looking because I'd like one rated to 500W).

5. Can I get a replacement flywheel?


That's up to the manufacturer.