Scotts Liquid Turf Builder with Plus 2 Weed Control is not labeled for St Augustine turfgrass. Please provide the type of St. Augustine turfgrass species that you have along with the weeds you wish to eradicate or prevent for a product recommendation. You can also contact your cooperative extension office if you are unsure of the weed or turf species.
Per the Product Label for the Scotts Liquid Turf Builder with Plus 2 Weed Control: A quart size bottle will cover about 6k sq/ft of a warm season lawn and about 4k sq/ft of a cool season lawn. We would not be able to tell you how long it will take for that bottle to empty as that is dependent on how fast you walk over your area and the output and pressure of your water hose.
Scotts Liquid Turf Builder with Plus 2 Weed Control should be hooked to a hose and will turn on and off. There is not a way to adjust the spray pattern.