No disassembly fix for a broken spring: Sling a rubber band under the trigger.

You do not need to remove the top two screws circled in red, just the four around the battery case (as shown in Step 13 and 14). Skip Step 12 which involves removing the plate.

As Rob said, don't pull it! The connector comes out vertically, not horizontally. The ridges along the side prevent the connector from sliding out horizontally. To remove it, insert a small screwdriver under the cables and gently push it to wedge the connector out. Connecting it is easier, just press it down over the top to snap it in place.