How can I draw over other apps?
In my old school days, this were trivial because just right behind the projector screen are whiteboards which is sometimes used as a "screen" which can be drawn on with markers. 

As more modern alternative, there are also smartboards that provides a virtual whiteboard to draw on with digital annotations. And one of them can be controlled and viewed from an Android tablet.

If you only need video and slides, then you can run your presentation on the computer running smartboard software and connect to the computer with the Android tablet controller. This doesn't actually allow you to draw over arbitrary apps though.