Brochure for Hybrid is 10.22m kerb to kerb, and 10.8m for Mk3.
Wouldn't be the the first time the brochure has been wrong.
The brochure is right: The Mk 3 Jazz turning circle is measured over the body, which is a worse case than kerb-to-kerb due to the body overhang.
The hybrid's electric motor helps the smooth starts more than it contributes to the fuel economy. You will have to get used to the Mk 3 needing to rev the engine above 3,000 rpm to get substantial power and decent acceleration (and then discover you are already over the speed limit).
1,100 miles in over a year is low to the extent if potentially bad if the engine has never been properly warmed up. Have a look at the mpg data in the trip computer (provided it hasn't been reset) as this could be a proxy for the usage pattern (very low (40 or less) mpg would indicate loads of short trips).
There is definitely an update or two for the infotainment system.