The preferred forms in the UK are "how long will it take?" and "how much time will you need?" The difference in the meaning is quite small, and there may be regional or cultural variations (eg between the US and the UK) in which is preferred. (Jim Reynolds might be correct in implying that the difference is not very important.)
As a native English speaker in the UK my preferences are :
- This is ok. Equally good is "How long did it take you to finish your homework?"
- Better would be "How much time will you need for the journey home?" or "How long will it take you to get home?"
- This is already good, but better is "How much time will the technical office need to fix my problem?"
- This should be either "How long will it take the technical office to fix my problem?" or the same as 3 above.