Objects can interact in many ways, that depends on the design.
In your case, click and box appears where is clicked, is not magic, you programmed it to do that, if you want to move slowly then you need to program that behaviour too.
get_pos
or get_global_pos
on 2D are used to get position, if you have a reference to a node (you can get it in many ways, depends on what you want to do and your design) just use those methods.
CollisionObjects (like Area) have _input_event
, if they have mouse event is because the mouse is on the area.
There are other ways, you can use Physics2DDirectSpaceState intersect methods and test mouse position to check if there is something in that point.
Once you "picked" a CollisionObject, make it "follow" the mouse pointer.
There are 2 official demos that use areas and pickable bodies that you can look to see how works.