1. Probably something like... IIRC The "UFO Power Source" from X-COM was a truncated cone with an orange-ish cylinder coming out the top. There you have an Elerium Collider in a generator.

2. I dare say having plenty of power would improve performance. But we've not really got any numbers on EVA strengths or power sources(relative size of Lucifer's colliders to say Eva-04's comes to mind). But hey, Let's not over examine this.

3. DJ's justification for naming Lucifer holds true and there are coincidences in the world. But by that point Lucifer had already been "talking" to DJ, so who knows what concepts and thoughts slipped in subconciously.