I think the clarification you need is that an "empty area" or a transparent layer does not contain pixels. Therefore, trying to "Move" a selected "area" does nothing. There is nothing to move.
In this example I make a selection, move the selection, choose the Move Tool, and get the "the selected area is empty" warning. This is because I am working on the top layer which is empty. I then select the underlying layer with the blue rectangle and am then able to move it.
Selecting an "area" of a transparent layer allows you to color, paint, etc. just inside that selected area. The "Lock Transparent Pixels" command in the Layers Panel locks all transparent pixels in the Layer whether they are selected or not.
It is possible to color a selected "area" of a transparent layer (a Layer with nothing on it). Then you can change those pixels to 0% Opacity (in the layers panel) and be able to move that selection, increase their Opacity, and they will have moved along with the selection. In other words you can have pixels with no Opacity that appear transparent, but they are still pixels that can be moved- as opposed to an empty "area" that contains no pixels.
I don't really understand your question about Image>Trim but it makes perfect sense that if there is nothing to Trim then nothing will happen.
Without some context to what you are actually trying to create here, the question is very broad and it's purpose is vague.
A suggestion- It is important that you ask one question at a time. Otherwise it makes it difficult to answer. More importantly, it makes it very hard for others to search and benefit from a specific answer in the future.