As to the first question, you can move a dynamic object if the tag’s “enabled” parameter is keyframed off, or if your timeline is at frame 0. Otherwise you can’t.
I don’t know why your bins started falling through the floor, unless the floor’s dynamics tag was keyframed off. Everything with a dynamics tag should interact with everything else. There are no separate domains in Cinema.
You might need to go to Edit>Project Settings>Dynamics>Advanced and increase “steps per frame” to prevent objects from falling through the floor or missing other objects. Some of the other issues might be fixed by increasing “interations per step” and/or by reducing the error threshold.