How to think about Power Factor when adding new devices to a generator
You need to look at both kW and kVA. The load must not exceed either. The kW limit is essentially an engine power limit. The kVA limit is essentially a generator current limit. The mismatch between the two assumes that the majority of uses have lower than 1.0 power factor and that 0.8 is about average. That means that the generator set is matched to that average. At that point, neither engine nor generator capacity is wasted. Engine-generator sets are also sold with kVA equal to kW. If the load has a higher power factor, that would be the better choice.

Detailed information about the engine generator set should tell how the ratings are limited by maximum temperature. There may be an altitude limit also. To some extent, operating below the maximum altitude may increase the maximum altitude limit.

Since current is the limiting factor for the generator, the highest current in any phase is the limit. I don't think lower current in the other two phases allows much if any excess current in the highest phase. The engine is limited by maximum total power. Imbalance among the phases probably doesn't matter very much to the engine.