Native AmE speaker -
It would not be wrong to say
Would their children chalk it in doorways before they know its meaning as a trademark?
But it is slightly different than saying
Would their children chalk it in doorways before they knew its meaning as a trademark?
in a way I can only really describe by example.
It is also different from your example of 'He went out before I had finished my sentence', although the end construction is similar.
Let's simplify the sentence since I'll be repeating it a lot -
Would John read the note before he left town?
This is someone asking a question about a hypothetical situation - perhaps someone's thinking of writing John a note, and is wondering whether it'd reach him in time. The situation could be entirely hypothetical - the note may not exist, John may have no plans to leave, or may not be in town at all at the moment. This construction implies the situation is something which could potentially happen in the future, and is wondering how that scenario would play out.
By constrast,
Would John read the note before he leaves town?
Is also slightly hypothetical, but implies that John is going to leave town at some point, and the speaker is wondering whether a note (which could be hypothetical) would reach him before he left.
It's such a minor difference that no one would probably notice the difference if you used them interchangeably, but it seems that people use the first way to refer to things that are more distant from reality, more hypothetical, and use the second way to talk about things that are only partially hypothetical, where that second part of the sentence is assumed to happen.
Now, the other quote you mention: "He went out before I had finished my sentence"
That's not talking about a hypothetical, and isn't a question, and so doesn't follow the guides mentioned above. It's fine as is, but changing it like:
He went out before I finish my sentence
Doesn't work at all.
If we make it a hypothetical question though,
Would he walk out before I finished my sentence?
It works, as does:
Would he walk out before I finish my sentence?
as well as
Would he walk out before I had finished my sentence?
(There's not much difference in meaning between those particular examples though)
For completeness, hopefully without adding confusion:
He would have walked out before I finish my sentence.
Doesn't work, because it's a hypothetical but not a question, and would need to be:
He would have walked out before I finished my sentence.
Or, more idiomatically for this particular situation,
He would have walked out before I could've finished my sentence.
or
He would have walked out before I had a chance to finish my sentence.
Will he walk out before I finished my sentence?
Is a question, but not a hypothetical, and doesn't work. It'd need to be:
Will he walk out before I finish my sentence?
If you'd like clarification/more details on any of those examples or constructions, let me know. If you're looking for the actual names of the different parts of speech in those different examples though, I won't be able to help, and you'll probably want to ask that specific question in the English stackexchange this question was originally posted to.
