I'll try to answer your questions from another perspective.
"Also, the answers seem to imply that there is a difference in meaning
between: "Как долго она не работала?" and "Сколько времени она не
Despite there's difference in form, the meaning is just the same.
And your another question:
"Is there any significance to the fact that perfective verbs are only
used with "за" and that imperfective verbs are only used in the
absence of "за"?"
I'd say, there's no significance to this fact. Let us see the examples:
Анна: За какое время ты сделала домашнее задание? (What time did it take you to do the homework)
Нина: Я сделала домашнее задание за час.
Imperfective verbs can be used with the preposition "за" as well.
Анна: За какое время ты делаешь домашнее задание? (What time does it take you to do the homework)
Нина: Я делаю домашнее задание за час.
"ЗА" in expressions relating to time means either "how much time does/did/will it take" e.g.: За какое время? За какой срок? or "for the time of smth e.g.: За время учебы. За время каникул.
In the situation you are concerned about:
Сколько времени ты делала домашнее задание? vs За сколько времени ты сделала домашнее задание?
Both the preposition "За" and a perfective aspect are used to highlight that the action is finished. But they are translated in the same way into English: How much time did it take you to do your homework?
And, also, probably some knowledge of aspect will help you investigate this puzzle.
(I suppose, you already know that, but, to my mind, it never hurts to revise). As well as in English, there are two aspects: perfective and imperfective.
Imerfective aspect has three tense forms:
(all of them are used when talking about incomplete actions)
The past form: Я делал /Eng: I did
The present form: Я делаю /Eng: I do/I am doing (and here it probably gets tricky)
The Future form: Я буду делать /Eng I will do
Perfective aspect has only two forms:
- The past form: Я сделал /Eng: either I did smth or I have done smth (BUT in Russian it's never about Present, in other words, it is NEVER about duration from the past until now. It is always about actions in the Past. This form is used when talking about completed actions)
- The present form: Я сделаю /Eng: I will have done it (it is always about the result in Future) It is tricky, because there's a present form, but a Future meaning. And again, we are takling about completed actions.
Hope that helps