Mat quality does NOT matter (bronze/ silver/ gold). Just get the cheapest. Exception to this seems to be 정령의 조화 for 응축되는 완전무결한 용석영, which apparently requires gold quality. Fortunately, gold quality 정령의 조화 IS the cheapest on the AH.
To teach the recipe to the crafter, you just target them and right click 고대 기억 in your bags. Using it makes it go on a 30 minute CD.
Recipe seems to disappear from the crafter after a while. Not sure of exact duration--it's under 24 hours. Maybe 12 hours? Crafter does get and keep a knowledge point for first craft of this, so that's a nice bonus for them.
If a crafter has 2 of the crafts listed (BS, eng, jc), it will randomly teach one and then refuse to teach the other when you recast it on them. This is based on what happened with friend's eng jc. Had to get him to use an alt with jc.

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Also, here is a cool weak aura (not mine, all credits to the author) for tracking all the mats you're collecting for 나스주로 - 해방된 유산:

간단 정보

스크린샷

동영상

영감의 질서 보정기

아이템 레벨 500
획득 시 귀속

요구 레벨 70
제작 재료
"함께 좀 더 강인해지고자 만들어진 도구입니다."

가이드