How would you say "questions" in Norse? How would the wrote it in runes? Does it has any important or philosophical meaning in the Eddas?
Questions have very important meaning in the Eddas; large parts of them are structured around a question-answer format (e.g. Gylfaginning in Snorri's Edda and Vafþrúðnismál in the Poetic Edda). This seems to have been a very common form for teaching and learning esoteric knowledge, and for showing off your learning.
Vafþrúðnismál is a good example, in which Odin goes to the ancient giant Vafþrúðnir to learn more about the world: the two of them engage in a competition about who knows the most of the universe. If Odin would fail, he would be forced to stay in Vafþrúðnir's hall for the rest of time, and ultimately he has to resort to a trick question: "What did Odin whisper in the ear of Baldr when he was laid on his funerary ship?".
As for the word would be, the base verb would probably be spyrja.