1) Yes, you can safely run the amp without a load. In fact, you should until you can power it up on the limiter without issue. Also, before you hook up a load/speaker, verify that there is no DC voltage on the speaker output.
2) My experience is that, much of the time the problem is shorted outputs only. I would check drivers to be safe and associated resistors. If you have it on limiter on initial power up, the bulb will tell you if there are more problems. Replace any known shorted/defective parts and try it on the limiter.
3) This failure can be caused by a multitude of things, so I hazard to guess. Probably the most common causes are a short presented at the speaker output or amp is driven past clip for extended periods of time. But again, it could be lots of things including no reason at all except a part just gave up.