Do Korea and Japan have their own national hashing standard? I know China has SM3 and SM4 commercial cryptographic hash and block cipher standards, and I know Japan has Camellia block cipher and Korea has SEED. Do Japan and Korea have an industry standard for hashing? Are they available online (either paid or free)?
Korea has its own standard for hash and block cipher, such as LSH (for hash) and ARIA (for block cipher). Source code can be found in here. I cannot find the English page, but google translator seems to work well. You can find information about standardization and other documents on the website, e.g. here.
The above-linked site KISA is itself authoritative and a public institute. If you want a much formal standard document, you could find them from TTA or KSA. The standard is as follows.

LSH hash: KS X 3262 KS Link, previously TTAK.KO-12.0276 (expired)
LEA encryption: TTAK.KO-12.0223 TTA Link but the document is mostly in Korean. Source code is available here but its manual is also in Korean.
ARIA encryption: KS X 1213-1 KS Link

The documents on KS site are not free, and they are also written in Korean.