Translation:I am listening because you are speaking.
Are there other verbs that conjugate similarly?
As far as I know, all verbs which start with what looks like a preposition or an adverb and which are accented on the first syllable in the infinitive are separable verbs -- the prefix separates from the verb stem and goes to the end of the sentence in a normal main clause.
For example, das sieht gut aus from aússehen, du hörst mir nie zu from zúhören, wann fangen wir endlich an? from ánfangen etc.
Whether the stress is on the prefix (and the verb is separable) or on the stem (and the verb is inseparable) is something you have to look up in the dictionary. Sometimes, there are even two verbs that are spelled the same but pronounced differently -- for example, úmfahren versus umfáhren.
Ich fahre die Katze um means "I will drive over the cat"; Ich umfahre die Katze means "I will drive around the cat".
There are some prefixes which are never stressed, though, and so verbs starting with a prefix such as zer-, ver-, be-, ge- will never be a separable verb.
In a subordinate clause, where the verb is at the end, it joins up again with the prefix -- since both are at the end.
For example: Er sagt, dass das gut aussieht. Er sagt, dass du mir nie zuhörst. Er sagt, dass wir jetzt endlich anfangen.
And Er sagt, dass ich die Katze umfahre is ambiguous between úmfahre and umfáhre.
Yes, lowercase sie can, as you wrote, also mean "she".
But this sentence uses uppercase Sie.
Furthermore, the verb form sprechen does not match sie "she"; it has to be either wir sprechen, sie sprechen, Sie sprechen (we speak, they speak, you speak). "she speaks" would be sie spricht.
Must "weil Sie sprechen" be translated as "because they speak"?
No, definitely not. Capitalised Sie means "you", not "they".
It must be translated as "because you speak".
Why is "while they speak" not accepted?
"because" (weil) and "while" (während) do not mean the same thing.
I am going by the last comments on this post. Some say that it is marked as incorrect. If you read it in the sense that "I am listening because YOU are speaking." makes it completely logical, meaning, if someone else were to be speaking, I would have immediately aufgehört zu hören!!