The split screen thing can be a little difficult to get out of... recall that there are actually two similar modes, split screen (with the black bar) and overlay mode (where the bigger window is visible on all sides of the smaller, guest window). I find that I have to convert a split screen into an overlay screen first by swiping down at the top of the smaller window, and then once I have an overlay screen I get rid of it by swiping it to the right off the display.
To answer part of your question, the way that it seems to work is that the way you switch between overlay mode and split screen is a downward swipe on the smaller window. This appears to work going in both directions.
As usual, imore.com has a pretty good explanation:
https://www.imore.com/how-use-slide-over-and-split-view-ipad-ios-11