The 7 speed button indicates you've bought a CVT Jazz. When you press the 7 speed button it basically gives you 7 simulated "gears" you can change between with the paddles, when it's off it's a normal CVT gearbox I believe. I'd be inclined to believe you have an issue with the gearbox if the judder disappears when it's in 7 speed mode (CVT's are notorious for failure and short lives on other cars, I'm not sure if the Jazz is the same - I believe I heard somethere where all mk1 Jazzes have some form of gearbox issues though, Manual or Auto!)
I doubt new fluid will fix it but could be worth a shot. Is there anything in the service history for gearbox oil? If it's never been serviced that could be why, depending on mileage.
Probably a 1.4 i-DSi CVT MK1 as the Mk1 Jazz has like... 6 configurations to choose from (1.2/1.4, Manual/CVT, SE/Sport)
Mk8 civic shares the same small L series engine so you probably know some things about it!