1. Here is an explanation of the nature of the dependent clause by Purdue.
(
https://owl.english.purdue.edu/owl/resource/598/01/)
Dependent Clause
A dependent clause is a group of words that contains a subject and verb but does not express a complete thought. A dependent clause cannot be a sentence. Often a dependent clause is marked by a dependent marker word.
When Jim studied in the Sweet Shop for his chemistry quiz . . . (What happened when he studied? The thought is incomplete.)
Dependent Marker Word
A dependent marker word is a word added to the beginning of an independent clause that makes it into a dependent clause.
When Jim studied in the Sweet Shop for his chemistry quiz, it was very noisy.
Some common dependent markers are: after, although, as, as if, because, before, even if, even though, if, in order to, since, though, unless, until, whatever, when, whenever, whether, and while.
2. Semicolon Usage
Taken from ---(
https://en.wikipedia.org/wiki/Semicolon)
One of the applications of the semicolon in English includes:
3. Between closely related independent clauses not conjoined with a coordinating conjunction, when the two clauses are balanced, opposed or contradictory:
• My wife would like tea; I would prefer coffee.
• I went to the basketball court; I was told it was closed for cleaning.
• I told Kate she's running for the hills; I wonder if she knew I was joking.
The Link between a Dependent Clause and an Independent Clause
When a dependent clause is used as an adjective or an adverb, it will usually be part of a complex sentence (i.e., a sentence with an independent clause and at least one dependent clause). The link between a dependent clause and an independent clause will often be a subordinating conjunction or a relative pronoun. For example
He literally stitched mail sacks
until his fingers bled. --
until is the subordiante conjunction.
So the second sentences in the choices A and B, while are related to the first, are not dependent clauses, since they lack the subordinating conjunctions.
HTH