Does the Torah instruct us to ask questions in search of wisdom? I understand that most of the Talmud is, in fact, questions and answers. But does it anywhere state that we must ask questions or be inquisitive and thereby find Wisdom?
I think you are correct that the unique question and answer approach of the Talmud demonstrates how absolutely basic this structure is in Judaism. Also, see how our greatest figures in Tanach, like Abraham and Moses, would even ask questions of G-d Himself.
Below are some sources that come to mind:
Exodus 3:4 – The explicit reason the Torah provides for why G-d spoke to Moses is that Moses chose to investigate an unusual phenomenon: “The Lord saw that he had turned to see, and God called to him from within the thorn bush, and He said, ‘Moses, Moses!’ And he [Moses] said, “Here I am!”
The Haggadah, composed specifically in question and answer form, is based on Exodus 13:14 – “And it will come to pass if your son asks you in the future, saying, ‘What is this?’ you shall say to him, ‘With a mighty hand did the Lord take us out of Egypt, out of the house of bondage.’”
Mishlei (Proverbs) 2:1-5: “My son, if you accept my words, and treasure my commandments, to make your ear attentive to wisdom, [if] you incline your heart to discernment; for, if you call for understanding [and] raise your voice for discernment, if you seek it like silver, and hunt for it like treasures, then you will understand the fear of the Lord, and you will find the knowledge of G-d.”
Talmud Makos 10a – “Rebbe said: Much Torah have I learned from my teachers, and more from my colleagues; and from my students more than all of them. ” This is referring the extra learning which comes from being questioned and challenged by others.
Talmud Tractate Bava Metzia 84a – Rav Yochanan lamented after Reish Lakish passed away that he could no longer learn Torah well because his current students would offer proofs supporting his arguments, while Reish Lakish used to vigorously challenge the validity of everything that Rav Yochanan said. Rav Yochanan exclaimed (to Rebbe Elazar ben P’das): When I would say a proof before Reish Lakish, he would raise twenty four difficulties with it. I would then retort with twenty four responses, which automatically expanded the understanding.
Keep asking questions!
Much success,
Shlomo Shulman
(Translation of verses from Judaica Press Tanach)