popup picture

Is it possible that when you scroll over a name from a game that you see in a popup the picture of the game

yes, if the image will be in a hidden <div>, you can show it using a short javascript function activated on  "mouseover" event... So, there are 2 things to modify: the block's php code (for the block which must contain the feature you require) - just make sure it reads the image name from the database; the second place - that block's html template - a container for images must be added.