Hi nhk9 san!
a. おんぞうし can mean "名門の子弟", but what does "おんぞうしくら" mean? If there's such a word... or maybe was that just "おんぞうしくらい"? I am not sure I heard the "i" sound though. The sentence from the drama is like "おんぞうしくら(い)紹介してもらえないか"
御曹司(おんぞうし) is usually means a son from a family of well-to-do.
A daughter of the same position is called 令嬢(れいじょう).
おんぞうしくらい=おんぞうし+くらい
くらい means degree/standard of things. It often used to suggest that something is not a big deal.
In the sentence you quoted, the speaker is saying
"You can introduce a son of a well-to-do family to me (which is not a big deal for you!)"
Similar usage:
転んだくらいで泣くな。
買い物くらい私だってできるよ。
b. Also, Japanese native high-school/middle school students wouldn't learn words like おんぞうし in class right? I suppose they would learn these via external sources?
You are right. Words such as 御曹司 is not a necessity of everyday life, though one can learn it from books and so on without being taught at school.
c. 揉め事 can mean "争い", but is this a popular usage? I haven't seen this many times before, but certainly I have seen "争い" many times though
揉め事 or its verb 揉める are often used.
It is similar in meaning to 争い but sounds smaller in scale and less serious.
(Though this is my personal feeling.)
It refers to the conflict/fuss/problem/difficulties between/among people.
d. Is わざとらしい a more colloquial version of the more common 不自然(な)?
I'm not sure which is more common but something わざとらしい is not something that just happened by accident but something someone did on purpose pretending it is accidental.
e. Is かどわかす a more informal way of saying "誘拐する"? I hear the latter much more often though, especially in newspapers.
かどわかす is rather an old word for 誘拐する.
It is used mainly in writing, it sounds old-fashioned compared with 誘拐する.
f. Is はめごろし considered to be an obscure word? (from はめごろし窓) It seems like it's one of those words that you never would know unless you really looked for it (or somehow came across it), if you are a foreigner.
嵌め殺し(はめごろし) is a fixed expression for window. The glass is fixed on the frame so you can see through it but you cannot open it.
Like the window on the plane.
エールコーポレーション株式会社