Calories don't matter (I know I'll get downvotes for that, but that's the truth).

You need to make sure you're eating enough food that provides you with the energy to do what you want without catabolizing your body. The only way to know that is to look over time how YOU look, feel, and perform. Are you leaning out to where you want to be? are you as strong as you want to be? are you as fast as you want to be? Are you progressing or are you back sliding? Are you tired all the time? Are you recovering from workouts fast enough? Only you know how you feel. Generally the if the answer is no to any of those questions, the solution is to eat more food. You just need to pick the right food for your activities.

I do a bunch of heavy crossfitesque metcons (too many, actually, I overtrain) and I'm eating nearly 5,000 calories a day. But I don't care about the calories (the only reason I know is that I was curious one day and just put my food into fitday), I make sure that I'm eating enough carbs (about a potato a day) to replenish my glycogen. I eat a ton of fat for energy and a ton of protein to rebuild my muscles.

Don't do silly thinks like avoiding a tablespoon of oil because it contains too many calories. That's the wrong way to think about it. If you need the fat (and I'm sure you do) for energy, go ahead and have some. If you're trying to lean out (and at 12% BF, you better not be thinking about leaning out), then you might want to be low on the fat intake temporarily just to get your body to burn its own fat. Post WOD, have some carbs to refill your glycogen stores. Eat more protein if you're not getting as strong as fast as you'd like or if your recovery is slow. Generally, I find that you can eat what you want and how much you want as long as you don't eat SAD food. Meat, veggies, starch, lots of fat - go ahead and eat what you want.

Basically, eat until you feel good and don't count calories. Just get as much nutrition as you can. Crossfitting 5 times a week is really hard on your body.

Are you hungry? Are you making progress with CF? I think these two questions are better indicators than the exact number of calories in terms of nutritional needs. I lean out consistently without counting calories, with somewhat CF-esque training.

12% bodyfat is pretty low for a female, especially if you're looking to maintain a high level of performance. It's tough to say exactly how many calories you need, as every individual differs, but without any other information, it seems like you might benefit from more calories. Don't forget they carbs, either—they're your friends when you're training hard.

I think your daily caloric intake is on the low end. Can I ask how tall you are? Also 12% bodyfat is near the bottom end of a healthy range for a female. Any lower and you might start having hormonal problems, and more so if you are restricting fat. At 80g Carbs per day, where are the other calories coming from? Just based on the info provided, you should prob be around 1800 Kcal per day, and prob 100g of protein.

Wow... I can't even begin. 12% bodyfat for a woman isn't lean, it's quite skinny, though if you were an ectomorph, that's fine. However, eating ~1300 calories a day doesn't mean you're an ectomorph, it means you're malnourished.../particularly/ whilst doing heavy training five times a week!!!!!!!!! Stop worry about a tablespoon of oil and see you don't need to worry about having too much fat in the slightest. Eat as much and of whatever (paleo) foods your body wants...it'll tell you how much fat and calories you need.

I would experiment and see how you feel. If you are constantly tired, you should up your daily calories by 100 and see if you feel better. Keep adding calories until you feel that you can fully recover and the you do not fizzle mid-WOD. Also experiment with carbs. I eat about 100 (not including fiber) per day, and I am a 5'1" female. I do not crossfit 5x per week, so you may need more. Also, everyone is a little different with nutritional needs. If you are happy with your current weight, don't be afraid to eat some fat. If you are trying to lean out, I wouldn't recommend adding fat like butter to your foods. However, you should still be eating fats that are naturally in food like fatty beef and whole eggs. Even if you are trying to lean out, don't cut fat too drastically since you need fat for the absorption of vitamins. Since you seem to be focused on the quality of your performance instead of leaning out, I would not be afraid to add in extra calories and fat if your workouts are starting to suffer.