I've learned that it doesn't hurt to have official logo variations, and here's why: on occasion, you'll have an opportunity to advertise with a logo but you might realize that in the particularly place you'd be advertising, there are many other logos that share similar characteristics. Happens all the time. Have foresight where you can.
Creativity is taking what is and bringing in what isn't.
A lot of these look like things I've seen before. I think you're on the right track for a clean and simple logo, but still needs more work. What if you took F and overlapped the dot and the "a"? I also like C on the second set, but I'm worried that the "a" might get lost with all of that black around it. I would say keep playing with the dot and "a" elements and the relationship between the two.