(6) the castoring nose-wheel can take some getting used to. It is easy to use the brakes to control direction on the ground, but I think better to use the rudder but this of course relies on a bit of airflow over the rudder (i.e. ground speed) and using pretty much full rudder.
After much experimentation, I found that the following works for me (in a DA-40 TDI, but
AFAIK the airframe is the same): I set the power for a reasonable taxi speed (1200-1300 rpm or abouts on the TDI) and then leave the power alone. This gives enough airflow over the rudder, even with a tailwind, to make most turns by using rudder alone. But I keep my toes on the brakes so that if I find that full rudder extension isn't enough to make the turn, I can instantly apply the brakes as well. I only apply the brakes without full rudder when I want to stop the aircraft in a straight line, or when I'm maneuvering in a really tight spot.
I used the one with the GFC700 autopilot which works great even in quite strong turbulence (enough to lift me out of the seat and bang my headset on the ceiling).
I have not experienced this myself, but I have heard that in strong turbulence it's better to put the A/P in VS 0 mode than in ALT mode.
An other thing I've found with the DA-40 TDI airframe is that once you get below 70 knots on final, the sink rate is much, much higher and takes almost full power to recover.
Oh, and in the cruise you might want to keep your feet lightly on the footrests instead of flat on the floor. There's not much friction in the rudder assembly (compared to aircraft with a steerable nosewheel) and if you just let the aircraft fly itself it gets into a Dutch-roll kind-of oscillation. Not much, not divergent and not dangerous, but just enough to be uncomfortable. Adding a little friction to the rudder system by keeping your feet on the pedals solves this. (And this also applies with the A/P engaged.)