Is it possible to access Shadow DOM elements through the parent document?

Question 1

@int32_t is right in that Shadow DOM, by definition, is a way to fill a node with DOM that you want to hide from external sources (Encapsulation). The point is that you as the component author get to choose exactly which parts will be exposed to outside CSS or JavaScript and which will not.

Unfortunately, you cannot create a public JavaScript interface to your Shadow DOM without using another bleeding-edge spec called Custom Elements. If you choose to do that, it's as simple as adding custom public methods to your element's prototype. From these you can access the internals of your Shadow DOM (see the third example here).

You can, however, expose hooks for CSS to access the internals of your Shadow DOM without using Custom Elements. There are two ways to do that:

Pseudo-elements
CSS Variables

Pseudo-elements

Chrome and Firefox expose certain parts of their Shadow DOM to CSS through special pseudo-elements. Here's your example of the date input with the addition of a CSS rule that only applies to the numerical part of the date field through use of the Chrome-provided -webkit-datetime-edit pseudo-element.

Here's a partial list of the available WebKit pseudo-elements. You can also just enable the Show Shadow DOM option in DevTools and look for attributes named pseudo.

Component authors can also create their own pseudo-elements to expose parts of their Shadow DOM (see the 2nd example here).

CSS Variables

An even better way is to use CSS Variables, which you can enable with Enable experimental WebKit features in about:flags in Chrome. Then check out this fiddle which uses CSS Variables to communicate to the Shadow DOM what color it should use for its "theme."

Question 2

Now (2016) you can access open user-created shadow DOM elements (but no user agent-created shadow DOM!) using the method querySelector on the Shadow DOM root:

<body>
    <div id="container"></div>
    <script>
        //Shadow Root
        ̶v̶a̶r̶ ̶r̶o̶o̶t̶ ̶=̶ ̶c̶o̶n̶t̶a̶i̶n̶e̶r̶.̶c̶r̶e̶a̶t̶e̶S̶h̶a̶d̶o̶w̶R̶o̶o̶t̶(̶)̶
        //new syntax:
        var root = container.attachShadow( { mode: "open" } )

        //Inside element
        var span = document.createElement( "span" )
        span.textContent = "i'm inside the Shadow DOM"
        span.id = "inside"
        root.appendChild( span )

        //Access inside element
        console.log( container.shadowRoot.querySelector( "#inside" ) )
    </script>
</body>

//Shadow Root
var root = container.createShadowRoot()

//Inside element
var span = document.createElement( "span" )
span.textContent = "i'm inside the Shadow DOM"
span.id = "inside"
root.appendChild( span )

//Access inside element
function get() 
{
  alert( container.shadowRoot.querySelector( "#inside" ).id )
}

<!DOCTYPE html>
<html>
<head>
    <title></title>
	<meta charset="utf-8" />
</head>
<body>
	<div id="container"></div>
    <button onclick="get()">Get</button>
	<script>
	</script>
</body>
</html>

Question 3

You can't access content of Shadow DOM from scripts outside of the Shadow DOM. Encapsulation is the purpose of Shadow DOM.

Question 4

Yes. You just have to call .root or .shadowRoot . Here's an example,

document.getElementById('itemId').root

You will not get the shadow dom element without the innerText or innerHTML on the parent dom element.