Thx for the basic theory of energy and chemistry. That clears up a lot of things in my head. So in terms of Chemistry and Physics goes, we are already reaching near the fundamental limits of energy storage?
Sort of, yes. You're not going to do much better than gasoline and air as long as you stick to the chemical realm.
However, there's still plenty of room for improvement within that limit. In particular:
1. The best batteries are still quite a bit below the energy density of gasoline+oxygen.
2. Creating batteries that can use stuff in the air the way gas engines do can let you "cheat" the energy density numbers.
3. There's a lot of room for improvements to how much batteries cost for any given capacity.
4. Similarly, there's a lot of room for improvements in battery longevity, in terms of how many charge cycles it can handle before it loses capacity.
5. Again similarly, there's a lot of room for improvement in charging speed.
I think 3-5 are key. Energy per mass or energy per volume is good enough for many applications now. It's not enough for airplanes yet, but as Tesla has shown, it's good enough for practical cars. The battery pack in a Model S is pretty heavy, but the fact that the rest of the drivetrain is so compact compensates a lot. The result is still heavier than a normal car, but not excessively so. The real limitations for electric cars are high cost (which is why the Tesla costs $70,000 and up, and cheaper electric cars have terrible range), battery replacement after some years of use (really just another dimension of cost), and slow charging speeds (meaning you have to wait 30 minutes or more for a charge, which is fine for normal city driving when you charge at home overnight, but troublesome for people who can't charge at home, or who are on a road trip).
I'm not aware of any fundamental physical limitations at play in those areas yet, and at this point they're probably more important than raw energy density.