Minecraft wiki entry for Beginner%27s_guide, associated text: Your cursor no longer controls your view. Instead, you use it to pick up and drag items among various slots. Left-click picks up or drops an entire stack; right-click picks up half of a stack or drop one item at a time. There are more complex options, see the "Inventory" article linked above for details.
Opening a GUI does not pause the game, but while you are attending to the inventory you can see only a little bit of the world around you. Be careful about fooling with your inventory while monsters are around! On the Java Edition, opening any GUI also allows you to switch away from Minecraft and to another desktop window, without pausing the game.