Do questions make life worth living?
Yes, questions make life worth living!
Questions are also the reason why we are presented of conveniences today, and some of these conveniences have made life worth living for some. Aside from the materialistic conveniences, having those also made us realize that there is more to life than possessing such. Questions make life interesting, the process of finding an answer to our questions can bring us to places we did not picture ourselves in (the thrill of uncertainty!).
The article below is as interesting as your question. Go and spare some time to read it.
Yes and for me the best answer is knowing that the meaning of life is God and our happiness. To day this can be understood although may not be a easy task. For more details see Abstract 1 of Life Philosophy by Joao Ferreira.