I'll try to answer your questions, as asked:
1. I do set my dahlias on some soil under lights to get them going. Some of them take several weeks to begin to sprout, others a few days.
2. As I said before, I do place my dahlias on to a bed of nice growing compound. I do lightly cover them, but don't bury them.
3. I think it is the heat and light that brings out the sprouts. The moisture of the growing compound definitely helps too. I keep this growing compount moist, but not wet, and thus it needs attention on a daily basis.
4. I do put a plastic cover over the container. Sometimes a plastic top which lets the light through, and sometimes a clear plastic bag.
5. I would let the tubers sprout some, and then you can separate if you feel confident. I would be tempted to gain some growing confidence before trying sprout cuttings.

I hope this helps.