does anyone knows, how to get the User ID who is the author of the discussion?
Are you still looking for an answer? What's the reason of your question/in which context do you need it? Just by looking at the discussions html?
You can get your ID by looking at your profile: https://open.vanillaforums.com/profile/warzyd.json
Now you know your UserID is 53927. With that knowledge, you can search the html and find it in multiple places. The UserID is enclosed in a JSON object, too. Try this in the console of your browser:
Depending on the way you access the page, you might want to try https://open.vanillaforums.com/discussion/38778.json to get the data in format that you can work with more easily.
That's the "frontend" way. Does that answer your question?