I have been reading about successful attacks on AES and other ciphers. One such mention is here (see excerpt below):
AES was published under the name Rijndael in 1998. Refereed cryptanalytic papers in the next three years culminated in attacks taking time "only" $2^{140}$ to break 7 rounds of 256-bit AES and "only" $2^{204}$ (with a huge amount of memory) to break 8 rounds of 256-bit AES. Subsequent work made very little progress. (Related-key attacks can break more rounds but are not of concern in any properly designed cryptographic protocol.)
I want to know:
If any paper mentions attack as $2^{140}$, how the researchers determine this number of operations?
Are these attacks only on paper or practically proven?
Considering super-computers owned by the government, which researchers don't have access, this figure may vary? Are these attacks taking into account super-computers computing power also?