I know the basics of splitting the screen/creating more of them. While I can split the windows at the right I can't do that on the left, because those typical lines on the left lower corner are missing. Can I make them appear somehow?
Find the dividing line between two windows where your cursor changes into a double arrow (horizontal or vertical). Right-click to activate the Area options menu which has two options: Split Area, and Join Area. You want Split Area. Then move your cursor into the window you would like to split.
In your case, there is no divider on the bottom or left, so you'll have to use the boundary on the top (between the 3D view and the info bar) or the right.