RE: Plane climbs after trim........
I had an Avistar as my trainer and it did the same thing. During my instruction, I was told that speed controls lift and elevator controls direction up or down. The faster you go the greater the climb rate. (At least on a trainer) All I did was trim the elevator to fly straight and level at 1/2 to 3/4 throttle, which is where I flew it during most of my training anyway. Like rcjon said, trim it and fly it before trying all the other stuff. IMHO