I have a direct question Is there any practical attacks on the AES cryptosystem (128-192-256 keys)
There are practical side-channel attacks against implementations of AES, but there are not any practical cryptanalytic attacks against the abstract algorithm.
The best cryptanalytic attack against the complete cipher in a reasonable attack model is probably the biclique attack, which only knocks a few bits off the key. The related key attacks against AES have attack models which are unreasonable when using AES as a block cipher to preserve confidentiality, and so are less/non applicable even though the bottom line of the computational cost of the attack is more pronounced.
For more information, you might investigate the following question/answers: How is encryption broken today? While that question/answer(s) is not specific towards AES, most if not all of the information is relevant.