How can Neo create games based on memories he never had?

Neo re-enacted the "storyline" the machines gave him. They kept him doped up and gave him fake memories.

Those where not memories that he was aware he had, so it's safer to say ideas implanted based on his memories.

And it doesn't matter if he experienced those or not, the machines obviously can implant memories and ideas.

Necessary to the Analyst's conceptualization of the Matrix. So in that sense, yes, necessary. But it was the Analyst's choice to go with that design, and it ended up outperforming all previous iterations of the Matrix so they stuck with it.

And that opens another question: HOW and WHY do they provide more energy (in the real world) than other humans???

Of course, that is on top of "how the fuck are humans a powerful and efficient source of energy???"

Specially since they just sit in those capsules doing basically nothing ...

Without even going into other questions like: how can a human with atrophic muscles even move when released from those capsules???

That isn't true at all. He knew about that, because he dreamed it. He could very easily have created a story that built to that point with different details along the way. It feels very obvious to me that that is what happened. Neo has dreams and flashbacks that he has incorporated into a game that is loosely based on what we know as the Matrix films. It's never stated, or even hinted, that the games are an exact scene-for-scene recreation of the films.

He could easily have included a scene in the game where Neo battles the Merovingian's minions, while two ghosts chase the others, but not include the ghost chase at all. Or, they are included but in a way that is only similar to what we saw. As long as the basic plot points remain the same-- Neo is the one, Agent Smith is replicating himself, the computers are attacking, etc., all the little moments can be radically different without changing a thing.