How can I play League of Legends at Korean server?

Not from there (from NA)

For the legitimacy, I've heard that a lot of Pros from CN and JP do train on KR servers, so even if its not legit, its at least tolerated.

For the creation: It does seem like in most asian countries, you need some resident code or a KR phone number to register. As much as it must be against TOS, there must be services that will create you an account on KR servers. Like I said in point 1, it's must not be legit, but probably is tolerated.

I'm from SEA and have played on all major Asian regions up to diamond/challenger.

You can create multiple accounts with 1 korean SSN, so if you have any korean friends, they can create an account for you.

Otherwise, you can try befriending some koreans on discord / other forums using monetary gifts.

If you're just there to test yourself, you can get a temporary account from any of the "korean account selling sites" that will likely get banned within a few months, enough time to squeeze a few hundred games in and get diamond+. You can find these sites easily via google. (A Chinese Kayn player managed to get rank1 earlier this season with such an account)

Since you're likely from Bangladesh, have you considered Ionia instead? It should be closer to you since it's located in southern China. You can get access by creating a QQ account and buying a VPN such as Xunyou.

You can also play on Garena TH or SG, both of which offers competitive games up to ~plat+