As a general rule, fireblocking or firestop should be installed anywhere a potential fire in a vertical space could jump into a horizontal space and spread to the rest of the building. The fireblocking halfway up on stud walls is there to slow the spread of fire through the wall cavity. By stopping the flow of oxygen to adjacent cavities, again, the fire would theoretically be slowed from spreading since the fire will burn towards the oxygen source. Effective firestops can be made with 2x dimensional lumber, 1/2" drywall, and/or rockwool. Installing blocking to the tops of walls is made easier with a nail gun or you can use screws and a power driver. As for the one inch gap, try to creatively use two pieces of 1/2" drywall to fill the one inch gap. Glue it in place, if necessary. Any wood fire blocking is not structural, and just a minimal amount of fastening is required to pass inspection. Rockwool is great for filling holes left by plumbers and electricians and for odd areas that otherwise can not be blocked with wood or drywall. Hope this helps....Good Luck.