An plays 24bits without downscaling?

Yes. I think it does

Hi! Could you check if it works with "Neutron MP". It's audiophile music player for android that has amazed me using a Galaxy Note 2 with a Pico DAC/Amp. I would like to know if you can install it on this player and how well it works. In advance, thank you.

I wouldn't recommend running any apps on it. If you do, it bypasses the awesome DAC chip.

When you find it sounds better than the DX100, how many hours was the DX100 burned in, and under which firmware was it running?

I'm not sure, but I compared it 2 weeks ago so it should be the latest firmware. I believe that the person who ad it has about 500 hours on it. I'll add comparisons to the AK100 and RWAK100 soon as well after using them at the melbourne meet.

How can an app (a software) bypass the DAC chip? I mean - the very hardware, that makes the digital files into analog signals which then are sent to either the line out or headphone out? This must be a misunderstanding.
What an app may compromise, however, is 24-bit file playback, since Andriod will downscale these to 16-bit. This is where the proprietary playback software comes in: It plays the 24-bits as they are without downsampling.