What app do Webtoon artists use to draw?

But to answer your question I think the majority of Webtoon artist uses procreate as the app and ipad as the medium, or they used photoshop and clipart studio. For me personally Autodesk sketchbook is a great alternative for a free software to use.

How do I learn manhwa art style?

You can try browsing through animes. Pick a few (or a lot) that catches your eye, specifically in style. You can then take out features you really like, such as the eyes, or the shading style, or maybe even the coloring style! Maybe start with the line art first.