1)
I have crudely measured power consumption on a 1997 Toyota Paseo (1.5L 4 cylinder). Starter power consumption is not anywhere near linear. It is a huge initial draw with a very quick drop off in power. I think the highest initial I saw was 300A but it quickly dropped to around 80A. This process took about 1 second if I remember correctly.
2)
The short answer I think is no, not really. It will start faster, but how much faster can it get? Starting takes about 2 seconds? I doubt it'll really get that much faster.
The reason that a larger battery will improve start up speed is due to voltage sag. As you increase the amperage load on a battery, the voltage sags farther. If you increase the capacity of the battery, the voltage does not sag as much. For example, lets say your stock Mirage battery sags down to 11V during starting. Now lets assume you use a gigantic battery and that voltage doesn't sag at all. It just stays at 12.7V. That is roughly 15% higher voltage. If that starts your car 15% faster (which is a big assumption). You've saved .3 seconds. Is that noticable?
3)
I personally haven't notice much difference. If my battery needs replacing, I'd check into a larger battery. I've looked into lifepo4, but the cost and the different charging voltage just doesn't seem to be a good fit.
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View my fuel log 2015 Mirage DE 1.2 manual: 47.2 mpg (US) ... 20.1 km/L ... 5.0 L/100 km ... 56.7 mpg (Imp)