Parts[] of DynamicModule output

I gave a partial answer to a question, Can Manipulate controls be generated programmatically based on a (non-manipulated) variable?, which has led me to questions of my own.

Background:

The following code produces a pair of identical Sliders, where setting a value of 1 shows up in the other.

   {Slider[Dynamic[d], {0, 1, 0.01}],
    Dynamic[d],
    Dynamic[Plot[Sin[1 + d x], {x, -10 [Pi], 10 [Pi]}]]
    } & /@ Range[2]

e.g.,

Wrapping the code in a DynamicModule gives you something different, the ability to set the Sliders independently (a possibly useful thing to do):

dm = DynamicModule[{d},
   {Slider[Dynamic[d], {0, 1, 0.01}],
    Dynamic[d],
    Dynamic[Plot[Sin[1 + d x], {x, -10 [Pi], 10 [Pi]}]]
    }] & /@ Range[2]

{"Length", Length[dm]}
{"Dimensions", Dimensions[dm]}
TreeForm[dm]

I’ve added the Length, Dimensions, and TreeForm to better understand what the code actually produces.

Let’s explore this a bit more:

dm[[1]]
Length[%]

Note, I set the Slider to 0.69 after executing the code.

And now I try to extract the Parts of the expression:

dm[[1, 1]]
dm[[1, 2]]
dm[[1, 3]]

This seems a bit strange.
I would have expected that I would get the 3 Parts of dm[[1]] in order, e.g:

Slider
Value
Plot

So, some questions:

1. Can someone explain this? The Parts of dm[[1]] don’t appear to behave as one would expect.

2. Does a way exist to access the current state of the 2 Plots in dm, and for instance Show them together?

3. Does the TreeForm give us any insight into how to do access Parts of such expressions?

I realize that these questions might resemble something akin to arcane chess problems, with not much real world application, but I hope that answers could give some additional working insight into these structures.

dm[[1]] // InputForm

DynamicModule[
  {d}, 
  {Slider[Dynamic[d], {0, 1, 0.01}], Dynamic[d], Dynamic[Plot[Sin[1 + d*x], {x, -10*Pi, 10*Pi}]]}, 
  DynamicModuleValues :> {}
]

DynamicModule[{x}, Slider @ Dynamic[x, (notScopedX = x = # )&]