"that" with embedded questions?

[dihen]

Would I seem foreign if I write "I don't know why did he do it."?

[dihen]

Is "I don't know who is [proper name]." acceptable?

Not really. It should be 'who [name] is'.

Why isn't it? Isn't it possible to say either "He is [name]." or "[name] is he/him."?
Therefore, "who" is the subject, not predicate, in "I don't know who is [name]."

Why?

Please answer this question. Why cannot "who" be the subject in this case?

[dihen]

Isn't this ambiguous?
`
"Who(m) do you want to leave here?"
can mean "You want who(m) to leave here?"
or "You want to leave who(m) here?"

Which would a native speaker usually interpret that as?

Please answer this question too. How would native speakers "deal with" a sentence like that?

[BobK]

"Who(m) do you want to leave here?"
Use either. In formal contexts, use 'whom', as it is the direct object of 'leave'. [There's a risk, though, that - if you use 'who' - any listener (formal or informal) may assume that it's the subject of the verb, and that you're making the mistake I warn about in red.]
can mean "You want who(m) to leave here?" Besides, if you said 'You want who to leave here' a native speaker would think that - as the syntax is foreign, but as 'who' seems like the subject of 'leave' - you were mispronouncing 'You want who to live here.'
or "You want to leave who(m) here?"OK if you put clear stress on the who(m). This sort of stressed echo-question is necessarily informal, so I'd expect 'who' in most cases.
Which would a native speaker usually interpret that as?

As my warning in red suggests, if you get the syntax wrong a native speaker may very well presume you've made the less fundamental error of getting the pronunciation wrong: 'leave' -> /li:v/ but 'live' -> /lıv/.

b

[MikeNewYork]

Would I seem foreign if I write "I don't know why did he do it."?

That depends. NNES are not the only ones who make errors. However, if that sentence were used by someone with an accent, the person would sound foreign and the error would be attributed to that, most likley.

[Tdol]

If you said it, though, it probably wouldn't come across as so foreign because that could easily be something a native speaker said, though much less likely in writing.