Looking for the grammar terms to describe the components of a question

Questions like these:

• "How do I increase productivity in my organization?"
• "How do I increase pro-social behavior in my community?"

I want to say that in all of these questions, the second part (e.g., "in my organization" or "in my community") is limiting the generality of the answer to the first part (e.g., "How do I increase productivity" or "How do I increase pro-social behavior"). In other words, I want to say that the answer to the first part of the sentence is dependent on the conditions of the second part .. so the answer is going to be relative, not in absolute terms.

What is the grammatical term for the first part and the second part of the sentence?

You are probably talking about theme and rheme. Those are not purely grammar terms, they rather concern the communicative structure of a statement. "In my organization" is rheme in your examples.