I've been wondering if there is any way to send a request to the site to determine if the site has 'index of' mode enabled; by that, I mean the site has all of the directories indexed (or part of visible directories).
Is there any way I could do it using HTTP requests in Python?
No.
The closest you could come would be to make requests to URLs on the site that ended in / and then run some heuristics to see if the format of the HTML document that came back matched the automatically generated index pages of various common web servers.
How to know if site has index of mode enabled in Python?