Seems like there are two different parts to this question.
- Show a transparent div over a video player
- Expanding the div to cover the player in fullscreen view
It's all possible, but only under certain conditions and with a fair bit of work. Most importantly, you need to have control over the way the video player's embedded in the page, and the video player needs to have a Javascript API that will trigger the resizing of the div.
If the video player is a Flash SWF, 1 is only possible if the SWF's embedded with a parameter "wmode" set to "opaque" (or "transparent"). Basically the wmode setting tells the Flash to act like a normal HTML element and not show through anything positioned on top of it. (More on this here.) On top of that, the video player must have a CSS "z-index" property lower than the z-index of your div. (The z-index is the stacking order, where 0 is the bottom and 1 is the layer above.)
As long as your video player container had position:relative, you could give your div position:absolute in CSS and position it relative to the video player with top and left properties.
Making the div transparent is also certainly doable. But it can get a bit complicated if you want it to be semi-transparent with content inside it that is opaque. Here's something on the CSS for transparency and details on the jiggery-pokery you need to do to make content show inside a translucent div.
There's an example here where elements have been layered on top of a JW Media Player, which will give you some idea how that part of it's done.
2 will require some Javascript, and it can be done with JQuery or Mootools, or just plain Javascript. Crucially, the video player needs to tell the rest of the page when it's resized to full screen: when that happens your Javascript can resize the div appropriately. Here's some code for another good video player, FlowPlayer, which shows how to listen for the "onFullScreen" event.
$f("player1", "flowplayer.swf", {
onFullScreen: function(){
// div resizing stuff here
}
});
Inside the onFullScreen function you'd put your code which resizes the div. You'd also need to use another listener to size it back down again when the player's shrunk back.