I think there is a lexical sensitivity to the choice between 에게 and the more formal and universal 에 의하여 (for 'by').
That is to say, most any active form can go into the passive and take 에 의하여. Your examples would become:
수프가 요리사에 의하여 섞이다.
문이 남자에 의하여 닫히다.
But only a subset of verbs can take 에게 (or more colloquially 한테) in addition to 에 의하여.
Would any ambiguity or conflict with existing grammatical rules arise? I know particles are often dropped in colloquial speech, but are nouns ever used without any case markers in proper grammatical language?
In Korean grammar, every case marker(격조사) is completely optional and it's perfectly "proper grammatical" usage to drop any case markers. In ...
에서 is not made of 에+서: on the contrary, 서 is considered a shortened form of more common 에서.
When describing places (i.e., where it happens), different verbs take either 에 or 에서. As HK Lee said, -에 is commonly used for verbs that denote a static state, while -에서 is used for activities.
In the sentence in question, "쓴다" is pretty active, so only -에서 is ...
I am not 100% sure on the logic for this usage, but I will add my ideas about it.
A phrase including 와의/과의 ("●●와의/과의 ◆◆") requires that these two nouns come before and after 와의/과의, respectively:
a noun (or pronoun) referring to a living thing (usually, a person or a group of people)
a verbifiable noun referring to an action or a result of ...
In addition to Usin Jung's answer, the difference is that 집(house) can be considered a place, but 풀(grass) is not.
Hence you can say "집에서 놀아요" or "집에 도착했어요", but you can't say "풀에서 놀아요" or "풀에 도착했어요." If you say the latter, people would probably think you're talking about a pool (수영장).
If you change 풀 to 풀밭 or 숲 then it's okay again (e.g., "곰은 풀밭에서 놀아요"), ...
"집 안" is more appropriate than "집 속". Everything else is fine. "속" contains the edges of the interior, while "안" represents the center of the interior. For another example, "물 속" is less awkward than "물 안".
Korean "-에" or "-에서" is similar to English "at". Therefore, "안" and "속" express additional meaning. Most of the time, it's okay not to use "안" or "속".
Usually 에 means 'state' : The money is in my pocket. 그 돈은 내 지갑에 있다.
And 에서 means 'activity' : I used to eat a meal at home. 나는
집에서 밥을 먹곤 했다.
I live in Seoul city. 나는 서울에서 살고 있다.
Lastly, 에서는 means 'comparing' : I saw a movie in his house. But it is impossible in my house,
because of father.
그의 집에서 영화를 봤다. 그러나
우리집에서는 아버지 때문에 불가능하다.