Is it possible to mix 4Ed powers into Essential builds & vice versa? IOW, could your Slayer take PHB fighter powers, or your Warlock take Hexblade powers?
In Theory, yes, assuming you have the slots for the power you're looking for. To use your example, a Slayer couldn't take Fighter Encounter or Daily attack powers,
as the slayer doesn't get them.
What abot going the other way, like the aforementioned Warlock taking Hexblade powers?
Same rule applies. If the right side of the power's colored bar (Class, level, type) matches a power you could already have, you can swap for it. If it doesn't, you can't. So anything that says "hexblade" or "feature" or doesn't list a level, your warlock can't have it.