I have somewhat extensive experience on this issue from driving 2 cars, one with a mechanical throttle (non-DBW) and another with an electronic throttle (DBW).
First, the biggest culprit in case of any drop in rpm or loss of engine power when anything that draws a current is switched on is the battery and its capacity in Ah. I frankly find it hilarious that Indus Motors takes the cheap approach of fitting their XLi's and GLi's with a tiny battery. I would strongly urge you guys to upgrade to a bigger battery. Aim for 55-65 Ah. Basically, the headlights, foglights, AC (blower and condenser fan), defogger, the EPS motor, etc, tend to suck significant electric power, in layman's terms, from the car when turned on. When the battery can not keep up with that increased power demand, the car's alternator has to do extra work to provide that extra electric power and if you know some basic EM Physics, as soon as the Alternator starts pumping out the much needed extra electricity, it's met by strong resistance by some magical forces (the details of which I won't go into). This explains the sudden drop in the engine's rpm when such an appliance is switched on.
Second, consumer cars with DBW/electronic throttle control are notorious around the world for have a time lag between pressing the gas peddle and getting the response from the engine.
Third, I believe that the issue of the RPM dropping when the clutch is pressed (during daytime, in the absence of any major electric appliance running) can be solved by increasing the idling RPM. This should be an easy job for your friendly neighborhood Toyota dealers armed with their OBD tool and some proprietary software. Insist on the idle RPM (when the car is at a standstill) to be set to 800-900. Trust me, it'll do wonders for you.
Fourth, now, this is a half-baked desi solution of mine, so try it at your own risk. When you know that you would need to stop at a signal or a stop sign or what have you, then as soon as you press the clutch to downshift to a lower gear, switch to Neutral altogether. Let go of the clutch and let inertia do its work. You won't have the dropping RPM syndrome with your car anymore.
Disclaimer: With the car in Neutral, you would have to rely solely on your brakes to bring the car to a stop since the engine's braking power won't be engaged anymore. Don't attempt this on slopes. Drive carefully and brake early, where necessary.