OK. To attempt to answer the questions:
1. The judges won't be disclosed until the competition has ended, in an attempt to keep things impartial.
2. I should have mentioned that the theremin is usually written for in standard, clef notation. It can be rendered on the final track as any solo instrument - a flute or ocarina should be suitable. If it's absolutely impossible to encode as MIDI, then concessions can be made.
3. I've created a thread for submissions here:
Submission Thread: Original Work for Theremin and Piano, though you could send an entry privately if you wish.
4. The competition is only being advertised here. It's small scale, and I only expect a handful of entries.
5. Copyright would be shared; both parties would have to seek the other's permission if they wished to publish the recording for financial gain.
If there are fewer than five entries, I'll consider extending the deadline.