Would it be possible to generate the original data from a SHA-512 checksum? So, I have a file that is XY Exabytes big. I create a SHA-512 hash from it.  

Are there any theoretical chances that I can retrieve the original data just from the sha512 hash?  

Also, are there any better hashes then sha512?
No, because a  hash behaves (simply put) like a lossy compression function. 

Meaning: you can use a hash like a sort of checksum, which enables you to identify and compare data. Using hashes, you can see if data has been modified (which, if re-hashed, would show a different hash as a result), or if two or more data packages are the same (every data package you hash will produce the same hash if the data is the same too).

But: you can not recreate the original data that was hashed. For that, you would need a (loss-less) compression function like you might know it from ZIP files. 

So, no, you can not recreate the original data from it's hash. The only thing a hash is good for is to compare it with other hashes to see if the hashed data is identical or not.

To give you a real-world perspective on hashing data and your question about "extracting" the original data from a hash: expecting someone to be able to reproduce the original data from a hash, would be like asking someone to create a nice dinner for all of us while only having a receipt available.

The only option to try to recreate data that results in a predefined hash, would be to "brute-force" it with a trail-and-error approach where you create random data sets, hash those, and hope that they produce the same hash you've got. While such a brute-force method works with small data packages, it won't work for big data-sets as you describe them since it would take too long until you "by chance" happen to produce exactly the same data-set that once existed and which produced the originalhash. Good luck with that... you can safely expect to waste a life-time trying to get that one lucky match that fits a specific, predefined hash.

While I'm at it: it might be interesting for you to know that older and mostly broken hashes (MD2 etc) are known to have certain weaknesses that result in so-called "hash collisions". Such hashes are broken because those hash collisions mean nothing else than  that two different data-sets produce the same hash, which should not happen as a hash is expected to produce a unique values for different data-sets. But that's just additional knowledge as hash collisions merely show the related hash fails it's job; they can not and will not help you recreate the data either. Why? Because a hash is something like an identification tag. It does not hold all the hashed data, and can therefore not reproduce it in any way.