I have Google searched this many times, but I only get "how to make a mobile version of your website" and such. I want to know if I am able to use my Android phone to write code/script and view the results. If so, how would I go about it?
Yes you can do this. You can install different Android apps to edit the code, any HTML editor tool will do - they can be found in the google play store.
You do not need to make a totally different version of your website, you can use google's mobile friendly test to check what needs to be changed.