That presupposes of course that there is a single spirit of Quora. There isn’t, any more than there is a single community on Quora; plenty of people here I can’t break bread with. For that matter, that presupposes that there is a spirit that is distinctively Quoran, which I’m unsure of; and I definitely think that Quora Inc has not had much to do with cultivating it. (It doesn’t get cultivated in a buffet.)
I’ll identify the spirit of Quora that I choose to subscribe to, as curiosity, helpfulness, and willingness to go beyond the superficial. That, you would hope, is the mark of the well-equipped citizen, and not just the user of a Q&A site. But we live on shifting sands now, and we get our Bildung where we can.
How do you carry it offline? Well, the helpfulness is sadly harder to pull off to your neighbour than to the anonymous peer online; but that, you can get to by having access to a group of people who ask questions, and don’t demand a Google-search one-liner for an answer. (A goal even D’Angelo has walked away from for Quora.)
The curiosity and the non-superficiality? Question things. Question what you see in the news. Question the givens of your culture. Question the easy answers. Suspect what narratives and interests and delusions underpin them. And come up with a framework to make sense of them, that works for you.
That isn’t about the spirit of Quora even, primarily. That’s about being a well-equipped citizen.