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Regarding the ticking, that's *probably* normal. The Insight's engine sounds like a sewing machine until it's really warmed up, with very audible valve noise. Once fully warm (long after the temperature gauge is stabilized at 6 bars) it gets to be in if the quieter Honda engines I've heard, but it still has its own unique character. I've never heard of any Insight having any bottom end issues, and the rare top end issues are generally catastrophic, like a broken camshaft.
It's really weird if it started on the 12v battery but still has assist. That would concern me. Typically these cars only use the backup starter when the IMA battery is really toast, completely empty, or when the temperature outside is lower than -4F(ish). Possibly a broken temperature sensor? Never heard of that though.
Auto stop will not work unless the climate control is set to "econ" or is turned off. If set to "Auto" it will disable auto-stop. I've also found that unplugging the climate control module in the back disables auto-stop, so one variable the ECU apparently requires is a "go-ahead" signal of sorts from the climate control, rather than a lack of a "don't auto-stop" signal.
Assist happens much less in 1st, but should still happen if you really mash the pedal and rev it up. It also secretly gives assist when first releasing the clutch but doesn't show this on the dash - it's far easier to stall a car in which assist doesn't work. Sounds like that was probably behaving normally.
I expect a Fit would get very little better city economy from a taller final drive, but might get (just going to make an educated guess) 10-30% better highway economy with a really tall top gear. I really like the Fit's engine, those cars have bad gearing for highway economy and the aerodynamics of a brick, but can still get 45+ on the highway with no special tricks.
K24 transmission with stock tire size will get:
50mph - 1645rpm
60mph - 1975rpm
70mph - 2300rpm
With an upsize to 185/70r14 (definitely the largest I would consider), it would be:
50mph - 1525rpm
60mph - 1880rpm
70mph - 2130rpm
Stock Insight transmission and tires deliver 2390rpm @ 70mph.
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