OK, I'll give a shot at clarifying these terms.
The key words to keep in mind are "
denied Dodge and Parry". This is the same as in D&D when you are
denied your Dex bonus to AC, although in Conan it is much more severe as it leaves you with a measly defense of 10.
"
Denied Dodge and Parry" are very often used interchangeably with the term flat-footed (I do it myself all the time), since they are quite similar. They are
not the same though, as we shall soon see.
So, a couple of situations and what happens in those situations:
*When you are flat-footed, you are "
denied Dodge and Parry". Also, you cannot make attacks of opportunity.
*When you are feinted, you are "
denied Dodge and Parry" (against that attack only of course).
*When you are grappled, you are "
denied Dodge and Parry" against other opponents than the one you are grappling with.
*When you are blinded, you are "
denied Dodge and Parry".
And so on.
Now sneak attack, for example, can be used against opponents who are "
denied Dodge and Parry" or who you are flanking, so sneak can apply in all of the above situations (and also against flanked opponents).
Another example, Uncanny Dodge, lets you "
still use Dodge and Parry when caught flat-footed or when struck by an invisible attacker". Ergo, Uncanny Dodge doesn't help you at all if you are feinted or grappled.
So in answer to the Brutal Attack feat, which I haven't seen myself (which sourcebook is it from?); if it says that it can only be used against flat-footed opponents, then no, it cannot be used against a feinted opponent. For that to be allowed it would have had to say "can be used against an opponent who is
denied Dodge and Parry".
I hope this made some sense, and didn't sound to snarky (it wasn't meant that way). Cheers!