<p>Akasha isn't an infinite well of energy. It's the Root of the universe, a complete record of the entire universe, past, present, and all possible timelines. Accessing it basically gives you admin access on the laws of physics in the universe, and you can change what's written in the Root.
</p><p>The Greater Grail is the system that runs the Grail War, does the summoning and everything. It does that by charging up energy from the land and starts a new war in around 60 years (or 10 for the fifth Grail War). The Lesser Grail is the recipient that gathers the energy left from the souls of defeated Servants.
</p><p>The point of the entire system is to accumulate enough of that energy to open a hole to the Akasha by brute force. The Lesser Grail stores that energy, the Greater Grail makes the system work. But since you have all that energy, at this point you can basically do anything you want even before opening a hole to the Akasha. This isn't really a function of either the Greater or Lesser Grail, it's just something you can do when you have such crazy amounts of energy stored.
</p><p>The five magics have nothing to do with the Grail War, apart from the fact that the guys who created the Grail system did so because they wanted to recover the Third Magic. But that was just an effect they could achieve by reaching the Akasha.
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