D&D Essentials is part of D&D 4th edition, and makes no differentiation as to source of feats. As essentials is entirely compatible, any character may take feats, utility powers (if appropriate), and items from the essentials books.
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However, it is important to note that the inclusion of any book or suppliment in an RPG is always subject to DM discretion, and so your DM may choose to disallow the book for any reason.
As a point of order it is not appropriate to give characters the new and improved expertise feats for free. Looking at the math here, DMs can draw their own conclusions about versatile expertise being necessary. The additional abilities granted by the new expertise feats, like ignoring cover, scaling damage, free actions to reload crossbows, and others, are beyond the scope of a simple math fix.