How do I apply a style to all children of an element

As commented by David Thomas, descendants of those child elements will (likely) inherit most of the styles assigned to those child elements.

You need to wrap your .myTestClass inside an element and apply the styles to descendants by adding .wrapper * descendant selector. Then, add .myTestClass > * child selector to apply the style to the elements children, not its grand children. For example like this:

JSFiddle - DEMO

.wrapper * {
    color: blue;
    margin: 0 100px; /* Only for demo */
}
.myTestClass > * {
    color:red;
    margin: 0 20px;
}

<div class="wrapper">
    <div class="myTestClass">Text 0
        <div>Text 1</div>
        <span>Text 1</span>
        <div>Text 1
            <p>Text 2</p>
            <div>Text 2</div>
        </div>
        <p>Text 1</p>
    </div>
    <div>Text 0</div>
</div>