Okay, first impressions with 2-3 hours burn-in. I played things I am familiar with using my normal amp (Hybrid - tube for input stage, FET output stage):
1 - Handles the HE-400 very well - no evidence of any problem with any aspect of the HE-400, and I could turn up "Keep On Growing" to the point where I knew the volume was not good for my ears.
This is what the specs (and the FAQ) would indicate. Should be plenty of power for the HE-400, and probably the HE-500 as well (although I do not own the latter).
2 - Very good bass response, not incredible, but good. Bass notes were clearly defined.
3 - A little transistor glare. This is where the burn-in may or may not have an effect. It could go away later, or it could be just what you get with a $99 transistor amp. This was more apparent on the SRH-1840 since it has more (as Mike would say) "technicalities".
At this point, I would say that it fits what you would expect - probably the best sound quality you can expect to get at $99, but don't trade in your $400 amp.
This is based on memory, I will want to plug back in the hybrid amp, and also compare to the cmoy, but that may take some more time. (The cmoy works with the SRH-1840 but not with the HE-400, by the way.)
Unfortunately, I have not heard any of the Fiio or "O" amps, so you will have to wait for someone who owns those for a comparison with those similar price point amps.