Can a platform offer a course of drawing in a specific art style of a modern work (that’s not in the public domain) without license?
I would say: even if it’s just a free video, C.Y.A. (wear some pants). At a minimum.
In other words, distance yourself from anything that ties to any sort of intellectual property. Don’t use their names in a title/description, don’t use their pixels (especially not in a thumbnail), use original designs and even add your own ideas or changes/improvements etc. Define, generalize, and abstract.
Keep any hint of it off of the internet until it’s finished and released.
Yeah, styles and ideas can’t be patented.
If you use it and sell it, you could be up for a trademark problem, like I can teach you how to draw the Nike logo, but you can’t then go on and make a nike-looking logo for your new shoe company.
This is on the very edges of copyright laws (and personality rights etc.), and therefore there are many different answers in many different countries.
Which country has a copyright law pertaining to art style? I’m almost 100% certain that OP is in the clear, regardless of where he is.