1. Does energy have dimensional size? This topic is not about area, but about energy, is it not?
What you're really asking is if the energy density for any point in space can be infinite. The answer is no. Ultimately the amount of energy a finite space can contain is limited by it's volume and is probably a function of Planck's constant.
2. I have long contended that the universe has no size with no boundaries according to my understanding of the definition of space.
And your understanding of space is informed by what? Astrophysicists at the University of Montana this year conducted an analysis of the cosmic background radiation that yielded a diameter of the universe of about 156 billion light years. This number must be regarded as extremely preliminary until verified by other teams of scientists, but the important point is that it reflects the thinking of experts in the field who, as shocking as this might seem, appear to disagree with your view that the universe has no size.
That's of course, another topic. Those who've debated this with me insist on a two dimensional model in their argument...
They used a two dimensional visual analogy because it's much easier to explain that way. If the analogy doesn't work for you that's one thing, but it doesn't mean they're claiming two dimensional models are appropriate for addressing problems in three dimensional space.
Any chance of this thread returning to the original topic?
--Percy