If installing a single Phocos Any-Grid PSW-H Hybrid Inverter (5kW) without batteries to start and if there is no battery connected and the solar input is less than the loads being powered when the utility grid fails, will that condition damage the inverter? The same question is true for the evening with no solar power and if the utility grid power is suddenly not working.

There are no precautions or safeguards that need to be made when using the Phocos Any-Grid PSW-H without a battery (single unit).  Regardless of whether the utility grid fails during night or day, the PSW-H will not be damaged, this is a normal operating condition. During the night, your connected AC loads at the AC output of the inverter will simply turn off when the utility grid fails, because there is no alternative power source. During the day, if the available PV power (minus losses) is greater than the total load power connected to the AC output, the PSW-H will keep supplying power to the loads, even without a battery and no grid power (the power comes from PV only). Please find more details about this unique feature here.