For 1, do you mean that you're listening to the onMouseMove event on a feature layer or graphic layer?
Ithink the problem is that the graphic highlight which is returned by the query/find draws as the top layer on the map, so the onMouseMove event doesn't react (since the mouse is over the new graphic, rather than the layer underneath.
You could retrieve attributes in the query/find, attach them to the new graphic, and listen to the onMouseMove event on this new graphic.
Is that what you mean?
Cheers,
Steve