Trying to build a house in Whiterun:

1) drag house from menu into render window
2) click and drag to move it

I can right click, rotate, and spin it, but cannot move or drop it. As soon as I press LMB, even with Z held down, it deselects the object and I cannot interact with it. Nor can I reselect it without 'undo'. Left clicking again deselects again.

Are you actually clicking on your house? Maybe you select another object instead?

You can see the selected object in the lower left corner.

You can also try to press E to open the movement Gizmo, it's a bit easier to move stuff this way.