Can I use Node.js for the back end and Python for the AI calculations?
Yes. That is possible. There are a few ways you can do this. You can use the child_process library, as mentioned above. Or, you can have a Python API that takes care of the AI stuff, which your Node app communicates with. 
The latter example is what I prefer as most my projects run on containers as micro services on Kubernates.
I am trying to create a website in Node.js. Though, as I am taking a course on how to use Artificial Intelligence and would like to implement such into my program. Therefore, I was wondering if it was feasible to connect Python Spyder to a Node.js based web application with somewhat ease.