I want to create a web app for my company that functions like a tool suite for non-technical employees to use. I'm using
Python
Selenium WebDriver,
BeautifulSoup,
Srapy,
Django
Is it possible and is this the right approach?
"The idea is to create a variety of methods that can be run by
  clicking a button and/or inserting content in inputs, and having the
  tests / functions run and returning the specified results."

Maybe Flask can help you here. It has a nice functionality to route urls to specific functions or methods in your code. It provides a convenient way to bind actions to code. You can search the web for how you can leverage Flask to cater to your specific needs, but here I just wanted to convey that it would help.
Selenium / Web crawling / Web scraping App in Python