It is theorised that the proposed cortisol lowering effects would be acute so take it when you would prefer to do this. Some people prefer first thing in the morning when cortisol is highest, I personal prefer after training because I tend to suffer from morning lethargy if I dose it the first way and don't need a full 3 cap daily dosage of Erase.
Empty stomach should be fine as far as I am aware, I have tried both and haven't had any side effects from either.
You could use Erase with ECA if you wanted. I personally do not like the ECA stack (don't like the traditional aspirin component) but stacking with stimulants is fine as a general rule.