What are the loads? I'm guessing they're not heating elements or light bulbs.
A pure inductor that is pulling 1kVA, a pure capacitor that is pulling 1kVA, a 1kW light bulb do not add up to 3kVA. In ideal system, it adds up to 1kVA. In reality, it adds up to slightly more than 1kVA due to I^2R losses in less than perfect cancellation of inductance and capacitance.
If you put a FULLY loaded 1hp motor and an idle 1hp motor, they do not add up fully either. The fully loaded motor acts more closer to resistive load and when you put the two loads together, the average power factor is higher. so you might have something like 1.5kW load with 2kVA.
We assume the source is a constant voltage and kVA is kV * A, so they are exactly proportional. I don't know what you mean here. Things that do not add up in current do not add up in kVA either, however watts ALWAYS add up independent of each other.