2D games are possible on a canvas. However, I believe those 3D games using HTML5 are actually embedded applications and not actually drawing on a canvas. Is that correct?

Answer 1

Basic 2D games are written in JavaScript but work on Canvases in HTML

Answer 2

No. The 3D games actually use WebGL for their rendering, and they are controlled using Javascript (much like the 2D canvas games).
No plugins are needed on modern browsers.

But there are projects like Unity and a sandbox for programs in Chrome, that do run the programs on an external application.

Answer 3

Learn three.js & ammo.js for 3d games.
(tree.js for 3d rendering & ammo.js for physics).You don't need a browser that supportes webGl.For some examples :
http://threejs.org/examples

Answer 4

yes

Answer 5

you mean games can be writing with HTML?

Answer 6

I don't think so because to write a game code we have to use an appropriate environnement prepared to.