The DA40 (I assume with the Thielert) is as easy to fly as any training aircraft, pleasant enough and a good work horse - if a little uninspiring. It is, in mine opinion, short on performance, which it makes up for in good aerodynamics, so once in the cruise it is reasonably quick. However, the aerodynamics don’t help in areas where there is no substitute for power.
There are only two differences to be aware of in operating the Thielert; instead of priming you need to lite the glow plug, and if you loose all electrical power you need to land pretty quickly because the engine will stop.
All in all there is not a great deal to flying a DA40 and a current and experienced pilot should feel comfortable after as little as an hour or two - perhaps just a bit longer if you have never used a stick before.
Turning to the G1000 this is as complex an avionics package as you will find in any light single - more complex than the Avidyne. It is a very capable piece of kit for serious IFR flying, even if the rest of the aircraft is not up to the job.
At its simplest, the primary instruments replicate the six pack. It may take an hour or two to get use to tapes rather than dials, and for some quite a number of hours before you are fully accustom to looking at a tape rather than a dial. However, ignoring the nav aspects you will be flying the instruments in VMC after a few hours.
We then get into the territory of how long is a piece of string. If your aim is to use the full functionality of the system this will take some time. If you are only “doing it” in the aircraft maybe ten hours and with a good instructor. That may seem a lot, but the test is whether you can program a route, select an approach, couple the route and approach to the autopilot and then “on the fly” change the route and the approach. There are a few gotchas as well which is were a good instructor comes into the game - and there are not many of those.
I think you are wasting a lot of time and making the task ten times harder learning this in the cockpit. Garmin provide a really excellent G1000 simulator. A few hours with the simulator on the PC is worth ten in the cockpit and you will have it cracked in no time.
Oh, and the KAP140 autopilot is OK, but not great if the going gets choppy, much as is the 40 which will not always give you the most comfortable of rides.