SACRIFICE SWARM: When an adjacent friendly character is KO'd or takes 3 damage but isn't KO'd, give Foot Elite an Opportunity token. FREE: Remove an Opportunity token to either make an attack or move up to 2 squares.

Basic CLOSE action - CLOSE: Make a close attack.

BLADES/CLAWS/FANGS When this character hits and would deal normal damage during a CLOSE action, you may roll a d6. If you do, deal damage equal to the result instead of normal damage. Minimum result is this character’s printed damage value -1.

Question

Can Foot Elite (Axe) use B/C/F with his FREE attack in his trait if the attack is from close?

No, BCF needs to be used on an attack during a CLOSE action. Sacrifice Swarm only grants an attack.

Yes and this is why Swashbuckling Sulu is worded differently:

Thanks. I thought it couldn’t but I just wanted to make sure. Still a great piece!

For what it's worth, this is one important distinction that helps players move from novice to experienced... CLOSE or RANGE (specifically all in caps) are the actions that typically activate powers and are referred to in caps, but close attack, ranged attack, or just "attack" are just attacks, not the caps. So any power that activates on a CLOSE (blades, flurry, quake, etc) will not activate from a close attack.

There are a handful of special powers as well as the standard powers Steal Energy (only from close) and Precision Strike (close or ranged) that work with attacks and don't need CLOSE/RANGE to activate so watch the wording closely and it will answer many of the questions about how powers work.

Ah that kinda lowers the appeal of the axe elite.

He's not any better or worse than the other elites in that respect... the dynamite one can't use EE with it, the hammer one can't use Quake, etc... but it's a free attack in any regard.