Say I declare I'm attacking with BCF, and I roll a 12. Do I add one damage to my blades roll?

Yep. 10 characters.

Yes, a critical hit will add to that damage. Since a critical hit adds 1 to the damage dealt, you would roll for BCF, and then the damage dealt would increase by 1.

And dont forget the knockback!

A lot of people forget knockback on critical hits. You would be doing d6+1 damage, so don't forget it, it could prove to be useful, especially if your target is on the edge of the building.

Knockback isn't mandatory on critical hits though - if you roll an 11 when using the And Stay Down feat or the Extraordinary Day BFC, no knockback would occur as it requires a roll of doubles.
It can still be cool - I remember a Legacy Battle Royale where Hyena Charged Hush, rolled a Critical Hit, and then rolled a 6 for damage, causing Hush to be knocked back into the "Shock the Turtle" Barrier and being knocked out. We all chanted "Six! Six Six! The number of the beast!" after that...

Sacrifice is going on tonight!

As I was so unpleasantly reminded last weekend.