How soon will you get back home? I am sure this question is correct. Can we ask if how soon you took to get back home or How soon did you take to get back home?
Yes, you can use how soon in the past, but it is not very common.
It doesn't fit with your examples, because how soon is an "at what time" kind of question, not a "how long" kind of question.
If you asked somebody "how soon did you get back home?", you would be implicitly putting yourself into the story alongside the person you were questioning. The information you are asking for would be the same as if you said "How quickly did you get back home?", but by using the forward-looking word "soon", you would be conveying something like "I'm imagining myself being back there with you".
Can we ask if how soon you took to get back home or How soon did you take to get back home?
Not exactly the way you have stated. Here are various alternatives:
How long did it take to get back home?
How long did it take you to get back home?
It took you how long?
Choice #3 is only to demonstrate the word "took" which you had mentioned.