In the course I taught at the community college over the summer, I did a variation of this. We only had class two nights per week and the class moved really quickly, so a weekly question didn't really fit with the schedule, but I made a list of essential questions that students needed to be able to answer in Spanish. The book for the course was very grammar-focused, so having the list of essential questions helped point the focus back to learning Spanish to communicate.
My weekly questions vary based on content. In Spanish 1 this week, our weekly question is ¿Cómo se escribe tu nombre? In Spanish 2, it's ¿Qué clases tomas?, and in Spanish 3/4 it's ¿Qué haces en un día típico? (and I clarify that I want them to name 3 things). Students sit in groups of 3-4 and ask and answer the question in their groups while I go around and talk to everyone. It does result in a few minutes of down time for larger classes since it takes me a little while to get around the class, but it's worth it to me to have that interaction with every student every day.