When I test it with a fresh scene I can't reproduce the issue. A red plane used as shadow catcher still reflects red onto a cube standing on it. It should actually be turned on by default but make sure that all day visibilities on the shadow catcher are enabled. If it still doesn't work please try again with a simple setup in a new scene to see if you can reproduce the problem. Also let us know the blender version you're using please.

Did you try copy from active in the rigid body menu from the top menu in the viewport?

Make sure that in the Field Weights panel of the cloth simulation all influences are set to 1. If you want more of a floating behaviour, you could however lower the gravity instead of counter the falling with a wind field. As for the force fields you may need to increase the strength. I quickly setup a sim with a subd-ed cube, a wind pointing upwards with a strength of 200 and a turbulence field with a strength of 1000 and size of 0.2. You could also watch a tutorial by Ian Hubert, who explains exactly what to do. He does indeed use soft bodies but maybe it helps you to figure out the setup.