As you can see in the picture, I have unchecked the spelling field. But for some reason it still puts this green "^^^^^^^^" under "wrong" spelled words. Which is very annoying.
What am I supposed to do, did I remove the green lines incorrectly?
(converting my comments to an answer)
From your screenshot, you clearly did click on the correct setting. There were two things I thought this could be. One of them was that, based on your screenshot, I wasn't sure if you had previously clicked OK on the menu, or if you had just clicked Apply. It turns out that if you click Apply, it doesn't actually take effect anyway until you click OK.
The second one (which it ended up being), was that there is a menu in Pycharm identical to the settings menu - the Default Settings menu. If you make changes there, they have no effect. In order for settings to immediately take effect, you have to edit them in the actual Settings menu (which can be opened with CTRL+ALT+S on Windows). Then, the setting is Editor -> Code Style -> Inspections -> Spelling -> Typo. You already knew that, though.