Can Darkness Within be used to boost the results of a BCF roll?

No. Darkness Within gives a +1 to your Damage Value. B/C/F then replaces your damage value with the results of a die roll.

Thanks for the clarification. Can you use Exploit Weakness with BCF?

Yes. BCF activates whenever you give the character a close combat action. EW is a close combat action, so it'll work. Same reason you can use BCF with Flurry (Flurry is a close combat action that grants two close combat attacks).