Caveat: 이해해 수 없는 한국말은 많아요

Lately it seems like I keep stumbling on Korean that my dictionaries can’t help me to understand.
Consider the notice found in the lower right on the webpage at the grade-entering application at work.
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I know from context that 등록된 원생이 없습니다 should translate roughly as “there is no one enrolled in this class,” but all the dictionary searches say that 원생 means “abiogenesis” (which is to say, the spontaneous genesis of life from non-life).  Which would give a translation more in line of:  “there is no enrolled abiogenesis.”  Hmmm…  So, I deduce that 원생 means “student” or “child,” which some understanding of how chinese-rooted words work makes at least a little bit of sense (I know 생 has to do with kids), as it would give: “there is no enrolled child.”  But it’s frustrating the dictionary won’t cooperate.  And babelfish, in this instance, concurs:  “There is not an abiogenesis which is registered,” it says.  Hahahum.
And I saw a sign in a cafe earlier, it said, in part, “다 드신 후!”  After that, it said, roughly, “please return your trays to the first floor.”  That second part, I translated and understood, almost effortlessly.  But that initial alert was completely impenetrable to me.  I can’t make any meaning of it whatsoever.  The dictionary is not useful.  Babelfish provides:  “after holding all…” which makes a little bit of sense, but I can’t really contextualize that either.
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