if I set up a var/www/site.com/node folder for strictly my node.js app files, I would be able to communicate between this folder and my site.com/public folder?

I think it depends on where/how you deploy to production vs development but not entirely sure. I have a node app deployed to heroku, but hosted on github pages. I'm not sure if you're familiar with those.
but when i was building it, i was connecting through the localhost. I think. haha
Brad Traversy on youtube has a good tutorial on node apps.