Do we have any idea as to how these cells, are able to work and the construction and power source it uses? Is it possible in our timeline or is it completely fictional? If there's guesses as to how these work, what are they?

Energy cell are probably just batteries, like the real ones. Probably using more advanced tech to store power. Real power cells produce power with a chemical reaction.

Microfusion Cell suggest there's a fusion reaction in the cell generating power.
With current real technology, fusion reactors are huge and they consume more energy than they produce. Additionally it requires extremely high temperatures and powerful magnetic fields to contain the plasma where the reaction happens, so it's completely fictional. Possibly based on the idea of Cold Fusion? That doesn't appear to be possible in reality, though.

Electron Charge Packs? It appears they are the most powerful of the portable energy source (possibly excluding Fission Batteries?), but there's really no hint on how they might work. Or if there is, i don't know about it

Just speculating here, of course.