Is it correct to say:
Please tell us the best choice, and why/why is that?
Tell me your name, and where are you from?
No. The second clause of both should be expressed as an indirect question:
Please tell us the best choice, and why/why that is.
Tell me your name, and where you are from.
You do not need the question mark and the awkward inversion and unsalvageable punctuation goes away.
16/01/21 Edit in response to a further point by the OP:
Thanks. But I specifically asked what is the rule here that won't allow it. Is it parallelism?
In a way, "Yes."
You should understand that there are two types of question, direct and indirect.
How about two question connected with "and": "What's your name, and where are you from?"
That is fine - 2 direct questions joined by a conjunction.
"Please tell us what your name is, and where you are from." = That is fine - 2 indirect questions joined by a conjunction.
You have tried to join a request and a direct question with a conjunction, and you can't do that...
If you look at your question, it should be obvious:
Please tell us the best choice, and why/why is that? = Please tell us the best choice, and please tell us why/why is that?
In Please tell us X, if "X" requests an answer/response (which your example does), then "X" is always an indirect question or request. "Why that is" is an indirect question, so that works... "Why is that?" is a direct question, and does not.