This is not an English-specific question. In Japanese, you might also ask "何時から何時までですか。" Or "nan ji kare nan ji made desu ka", "From what time to what time?" (from Google)
Sometimes in daily conversation you might hear someone ask "How many people are going in whose car"? Or "Where did you buy what from?". To which the response might be "Six people are going in Bob's car" or "I bought ice cream. I bought it from the shop over there".
This can happen when someone has two questions to ask. The meaning is often perfectly clear to the person being asked the question and they are then able to respond by answering both questions in one or multiple sentences.
So the first thing I want to suggest is that these sentences don't break any natural rules of communication, aside from being a little cumbersome. However, they might not be "formally correct" in the grammar of any given language. Are there any formal rules of grammar which they break?
Personally, have you heard someone ask multiple questions this way before?
Note: There is another way to combine two questions into one sentence, using "and". What I'm talking about is different from asking "How many people are going, and whose car are they going in?" or "What did you buy, and where from"?