How low can I set my percentage of calories from fat — I'm aiming for 10 to 15 percent?

Percentages are not the best way to look at this. You say ... you are aiming at 10-15% fat. Let's think about that for a moment.

On a cutting diet, when I consume 1800 calories, 10% fat would be 180 calories or roughly 20 grams of fat.

On a bulking diet, when I consume, say, 4200 calories, 10% fat would be 420 calories or roughly 45 grams of fat - nearly double the first example.

Does your fat intake/requirement really vary that much depending on your goals? I doubt it. I'm sure there is a minimum amount of fat required to reapir cell membranes, regulate hormone function, etc. Beyond that, some may be required for energy during endurance events. Then, it should be relatively fixed regardless of if you are gaining or losing.

Now, Udo Erasmus has a few recommendations, namely about 1 tsp per 15 pounds or 1 tbsp per 45 pounds of weight. This would be roughly 14 grams per 45 pounds or 1/4 cup of whole nuts, for example. These are just estimates.

Your question is really one that people will debate and argue, but hasn't been answered. Personally, I avoid excess land-animal saturated fats. This means the fat in red meat, chicken, etc. Other fats - what is naturally in grains and vegetables, what occurs in egg yolks, what you find in cocunut oils, etc - I don't worry about. I allow these into my plan and instead of worrying about ratios or percentages, focus on total calories based on my goals.

If I am cutting or not eating plenty of cold water fish, etc, then taking on a few extra tablespoons of healthy fats per day seems to help.

Basically, if you cut fat too low, you risk losing natural testosterone production and inhibiting your ability to recover from exercise. Hormones are manufactured from fats and cell membranes are made from fats and cannot be repaired if sufficient fats are not supplied.

Therefore, a good strategy is not to buy into the old, outdated notion that cutting fats is the key to fat loss - it's not. Cutting calories and increasing energy expenditure is the key, and where you get those ratios from is more a function of your body weight than some magical ratio or percentage.