Does a Essential Fighter (Slayer and/or Knight) meet the Prerequisite "Fighter" for the purpose of taking Feats?
Yes, all Fighters are Fighters.
If a feat has "Fighter" as a prerequisite, any kind of Fighter suffices: Weaponmaster, Knight, Slayer, hybrid, multiclass. This is a clever way for Wizards to avoid having to create two unique sets of class feats that are effectively identical to a set they've already made. They did the same thing for Wizards, Druids, etc.
It does create some odd wibbly bits where you can qualify for a feat that enhances features you don't have--in which case the feat is useless, but you could still take it if you want.