South Korea Temporary stay visa waver and working holiday visas

Hello all, I have a query regarding visa wavers and working holiday visas.

I have currently been using temporary visa wavers 90 days as I am a United Kingdom citizen for the past 9 months.
I called up immigration and they said this was ok, as long as I wasn't working. If I was stopped at customs or immigration it was only due to suspicion that I may be working after the short holidays I took in and out to allow a new 90 day lease to continue.

I have considered taking part in a Hagwon for Korean language and have studied Korean enough to get by fairly comfortably. My girlfriend is Korea which is the main incentive why I am in South Korea.

Now the first query I have is, ive heard that in Korea that it depends on which immigration worker you call or get or something, apparently they all say something different depending on mood.. which to me seems totally ludicrous, I'm sure this immigration worker i called was correct and want to trust what she said. I just wanted a second more experienced opinion so I cant be blamed.. if anything did go amiss.

Secondly, in Japan someone can work in the English field part time, private, eikawa's like hagwons equivalent etc and I hear that this is strictly prohibited in Korea. I've read some pretty terrible stories of people being treated like criminals when sometimes the laws of Korea seem almost invisible.. obscured.. apply to some but not to others.. or just benefiting Koreans and not foreign people.
I wonder to what extent the work one can procure in Korea say Jeju is possible to obtain on a H1.
I don't want to break the law, ive never been for breaking the law.. even stupid, nonsensical laws that seem to benefit the rich or small strata's of society such as what ive heard when it comes to teaching in all its forms in Korea.. however due to just how vague that topic seems, how grey, invisible or biased to Korean favour I wanted to know your thoughts?

Thank you for your time.

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