On watering, I water potted hems daily adding water to the rim of the pot and letting it run through twice. For hems planted in the ground in shade I water every other day for 10 minutes on pop up shrub heads (Toro). For those in ground in full sun they get 6-8 minutes daily. I also have seedlings on drip irrigation in raised beds. My drip runs 2 hours every other day with once a week drenching by hand. This ensures even distribution since gravity pulls drip water straight down with limited capillary spread.
As far as how many inches of water a single gallon might provide, this is a tricky application of math that would depend upon your distribution method and area of coverage. One gallon of water might cover 1" in 1 square foot of coverage, however, water moves through the soil disproportionately from the application site. Established clumps of differing sizes would require different quantities of water depending upon upon but not limited to the following factors, number of fans, height of foliage growth, spread of foliage growth, quantity of scapes/Blossoms produced, number of pods set, sun/shade exposure, context of soil, friability of soil, drainage of site, exposure to elemental factors such as wind or breeze, competition from surrounding plants, underground inhabitants of soil (tunnels crated by voles, moles, gophers, mole crickets, and earthworms all affect distribution of moisture), use of mulch, type of nutrients provided.
On nutrition, I do not fertilize my gardens, shrubs, trees, production beds or lawns. I do not purchase fertilizers. I use natural organic nutrient compounds inoculated with beneficial microbes. I feed with these nutrients every 6-8 weeks depending upon growth rate, leaching, and soil quality. I do not worry about heat stress or burn because I feed without fertilizers.
On heat, heat affects each garden bed or site differently depending largely on soil context and air spaces within the soil. Clay soils contain very low oxygen holding capacity and far less water holding capacity than you realize. Stones, gravel, wood chips and other heat conducting particles collect and release heat that soil free of these elements would not experience. Clay particles are flat (silt) and also heat up more than loam. Incorporating loose organic matter of various texture types ensures ample air spaces to radiate heat out and keep the soil cool. Mulch also shades the soil and aides in moisture retention, but can be harmful to hems in clay soil, particularly if heaped too close to the crown. Water is a heat conductor as well so should be applied early with ample time to dissipate into the surrounding soil and leave those air spaces open to regulate soil temperature before the sun reaches the soil. When I hand water, I never do it mid day, in full sun or during peak heat times. Morning is best, earlier is better. If you can't hand water early in the day, wait for the heat of the day to pass. It's best not to water after nightfall. Let your hems dry before night.