Ok, this is kind of complidated to describe in just words, but I’ll give it ago.
The Slide Over app is persistant. What this means is that once you place an app in slide over mode, it stays in that view/mode until you either place another app in slide over, or you force the current slide over app into full or split screen.
So, once an app is in Slide Over you can place it over any current app(s) byTapping on the slide over app or
Swiping left from the center of the right edge.
You dismiss it (while leveing it in slide over mode) by draging the top tab to the right edge of the screen.
This can be really annoying, if you are not expectring it. But it can also be very handy. Because it is persistant, you can keep using this same app over multiple apps (full screen or split view). For instance, lets say you want to gather notes from multiple sources (Safari, PDF, and Word). If you place the Notes app you can keep using it over the top of all these documents, sliding it out of the way or to the other side of the screen when needed.j
Another use for this are the new Shelf apps. You use these like a supper clipboard; moving from app to app, dragging content into the shelf. When you’ve got what you want you open the destination app(s) and drag the content back out.
Split view mode is harder to use this way. While split views are persistant, they can not be duplicated. Once you creat a split view (say Safari and Notes) each time you tap on those apps they will open back in split view. However, if you use either of those apps in full view or paired with another app, that split view is broken in favor of the new fulls screen or split view.
So the persistance of slide over is both annoying (when you do not expect it) but very handy once you understand how it works. The slide over app becomes your go to app for stuff you want quicly available. At least untill you decide you want a different persistant app in slide over.
For your second questions, this is trickier, but again, harder to describe than do.
Tap and hold on the first apps. When it lifts from the screen drag it just a bit (but not on top of another app). Without letting go of the original app, tap on the other app you want to use. The second app will open, and the first app will now appear as on top as a retangle. If you want it to be in slide over, drop it in the middle. If you want it in side view, drag it to the right or left edge of the screen. The screen boarder will widen to show you that you can drop the app there.
Note, that if either of the apps you are trying to split are not able to split, you will only get the slide over option (or neither if the top app can’t be put into slideover). There are still a few apps that are not multitaks enabled.
A trick to keep you from having to pair accross multiple home screens (difficult but possible) is to take the extra apps you only occationally use in split view and place them in a folder in the Dock. It’s not a great solution, but it works.
There are several videos showing how to use the new multitasking enviroment in iOS 11. I recommend searching either Google or YouTube for iOS 11 multitasking demos or turtorials.