How long will you stay and where ?
How long and where will you stay ?
In which sentence is the placement of where used correctly ? Or both of them are the same ?
Let's look at the definitions first:
Interrogative Pronouns: The main interrogative pronouns are "what," "which," "who," "whom," and "whose." Interrogative pronouns are used to ask questions.
Do not confuse interrogative pronouns with interrogative determiners (called "interrogative adjectives" in traditional grammar), which look the same as interrogative pronouns.
Interrogative determiners modify nouns or pronouns. Look at these three questions:
Which route is the safest?
What food are they buying?
Whose one shall we take?
Do Not Confuse Interrogative Pronouns with Interrogative Adverbs The interrogative adverbs are "why," "where," "when," and "how." Interrogative adverbs are also used to ask questions, but the answers to the questions they ask are adverbs. The answer to a question starting with an interrogative pronoun (or an interrogative determiner) is always a noun. You could use a stand alone interrogative adv at the end of a question (like your first example) or you could use it in phrase (see the example below)
who are you? - Mike.
this is an interrogative pronoun.
whose book is this -? Mich's
this is an interrogative adj.
who are you and how did you get here - by breaking the window!
this is an interrogative adverb.
so, The answer to a question starting with an interrogative pronoun will be a noun (typically a person, place, or thing). The answer to a question starting with an interrogative adverb ("how," "when," "why," "where") will be an adverb (typically a place, a manner, a time, or a reason).
Now to answer your question, your first sentence uses "where" as an interrogative adverb:
how long will you stay and where? I'll stay for 2 weeks and in my dad's cabin
the second sentence where along with how long are interrogative pronouns:
how long and where will you stay? I'll stay for 2 weeks and in my dad's cabin.
as you can see the answer to both are the same, but on a technical level they are more nuanced.
ref: https://www.grammar-monster.com/glossary/interrogative_pronouns.htm