Mvars and System Voltage

I will add some information only to this part of your question

"why do capacitors produce and inductors absorb?Э

In capacitor the current first reaches the plates which builds up the voltage across the plates of the capacitor. Hence the current is leading the voltage and because of this reason the capacitors are considered to be a source of reactive power and also the reactive power in this case is considered to be negative.
vise versa to the capacitor, in inductors voltage is leading the current and the power is stored by inductors only because of their magnetic fields to keep current constant and they expand and collapse. Since the alternating current changes, the expansion and collapse in magnetic fields and electrostatic happens.

let me also mention one more thing in your question. Please check this part of your question,

"triangle (VA = sqr(MW^2 + MVar^2)"

Just change VA to MVA

The KVAr largely depend on the angle 0₁ of the entire load (Power rating) in MVA. The lagging phase angle in this case is as a result of various form of inductive loads.The more the inductive load, the wider the phase angle 0₁, and the lesser the inductive load the lesser the phase angle.

The KVAr(BA) is a function of the phase angle.The more the phase angle , the more the the KVAr and vise versa.

A capacitor injects power in the direction of the arrow as shown in the power triangle below. If, for example, BA is 600KVAr and we have a capacitor of banks C, D and E that are 200KVAr each, you will notice that as the first banks is switched in, the new KVAr becomes CA and the phase angle is 0₂. The action taken here is 600KVAr - the injected 200KVAr. When the KVAr is D (400 KVAr), injecting/adding another 200KVAr brings the KVAr to E(200 KVAr). At this point, the MVA is OE, at a very little angle 0₄. EA is the very little MVAr that can be ignored.

At any moment when the MVAr is at point A, we assume unity power factor and at this point in time, MVA = MWA and PF = 1(unity)

NOTE: MWA = OA, MVA = OB, MVAr = BA

DICKSON.

There is a fundamental misconception in your post. There are 2 types of MVARs, leading and lagging. "Leading" and "lagging" refer to the position of the current sine wave with respect to the voltage sine wave. Capacitors and inductors both act as absorbers and as producers of MVARs, but they are 180° out of phase with each other. Capacitors produce during the half-cycle when inductors are absorbing. In the opposite half-cycle, inductors produce while capacitors absorb. In practical application, the capacitive and inductive MVARs cancel each other when the quantities are equal. The cancellation is observed in the external circuit, not in the between them. Between the capacitor & inductor there is a continuous circulating current.

Most non-resistive load is inductive (transformers, motors, solenoids, etc. are all inductors), distribution systems tend to have a lagging (inductive) power factor. All of the leading MVARs are canceled by the lagging MVARs, with some lagging MVARs left over. People tend to discuss only "what's left" and therefore refer to all MVARs as lagging - thus the statement that capacitors produce MVARs and inductors absorb them.

Another idea to consider, which may help with understanding: the power triangle you describe can be on either side of the Real axis, depending on whether the reactive power is capacitive or inductive. The absolute values work out the same, but the sign of the MVAR value will depend on the dominant type of MVARs in the circuit.