Opening the app switcher is essentially a gesture. As is opening quick settings. Opening notifications makes a little more sense as notifications appear at the top of the screen. Rearranging the home screen is also a gesture.
A long press on the icon you want to move and you've picked it up (it comes "closer" to you and moves to be exactly under your finger). Drag it around and other icons will move around to preview/indicate where it'd be. Let go and it drops into place. There is no jiggling. You can also drag to Remove or Uninstall (Remove leaves it in the alphabetical app drawer).
Creating folders is the same as iPhone.
There is a caveat that if the icon was held very still then you'll open a menu similar to 3D touch menu. I never use this because it isn't that discoverable.
I think it's probably okay that quitting apps isn't that obvious; under most circumstances you don't need to quit iOS apps. Only very specific kinds of activities are allowed to run in the background; when you switch away from an app and don't switch back to it, it's going to be force quit by the system when it needs resources. Managing iOS apps like desktop apps is kind of an anti-pattern.
I agree about point #1, but I'm also not sure how to make copy/paste particularly obvious with touch. To be fair it's not really obvious with a mouse or other external pointing device -- it's something we just have to learn.
