These days we have an official Q&A plugin, see: Discourse Question Answer
That said reading your description this is not a software problem you are facing. It sounds like you have a non cohesive community problem … too many avenues for not enough people.
For very small communities just leaning on GitHub for everything may be all you need, Discourse certainly gives you more features, but all the features in the world are not going to fix a people problem.
Discourse could work for you if you keep bugs/features/questions all in one roof, but if people need to read a manual to figure out where each category lives then it can be very problematic.