Ok.

So my 1.8L WAS making insufficient power to handle the A/C load, combined with running both the cooling fans at idle.

So my deduction that the Engine jerks when there is load on the engine at idle is due to insufficient power hold correct.

But the reason why it was making low power was due to a vacuum leak caused by leaky intake manifold gasket, which was identified by a Mazda Elite dealership.

My solution to the problem is over here

Solution

Actually there were 4 problems, which appear to be different, but were solved by replacing the intake manifold gasket.

they were:

1. Engine jerks due to momentary stall at idle when load is increased such as A/C compressor engaging + both cooling fans running.

2. Automatic transmission giving a distinct clunk sound when shifting to 1st gear, coming to a stop.

3. Transmission unable to engage cleanly when doing a running STOP viz. slow down to about 3mph at a stop sign and step on the gas pedal would give me a lag and then "WHAM" the gear would engage

4. Erratic idle, flutters when Headlights are switched on.