How much fat to eat to absorb vitamin D and how many total calories per day to lose weight. (To Anonymous)

In reply to your lovely questions I think it necessary to understand the premise of calorie (calorie=Kilocalorie) content of food: food calorie content is usually assessed by totaling the calories of the individual nutrients of a given food. For example the calorie production of protein is assessed to be 4 calories per gram, and that of fat as 9 calories per gram, and carbohydrates 4 calories per gram.[Food Energy [1]] These estimates for the individual food nutrients are done by direct calorimetry as follows: 

Merck Manual - Home Edition [2]

This to me this is a very imprecise, unscientific way of estimating calorie content in food as it translates into energy or fat storage for the human body. The body is not a bomb calorimeter and as such translating or equating 1 gram of fat to 9 Calories of energy that will be stored as fat is pretty naive (on the part of the authorities, scientific or governmental). The support for my statement above is evidenced by more than one study, but my favorite is in a study published in the Annals of Internal Medicine in 2010 where it was clearly seen that successful weight loss can be achieved with either a low-fat low-calorie or low-carbohydrate unlimited calorie diet when coupled with behavioral treatment.[3] Focus here on unlimited calorie intake of fat and protein. Another study in support of my statement included the Atkins diet where it was seen: women assigned to follow the Atkins diet, which had the lowest carbohydrate intake, lost more weight and experienced more favorable overall metabolic effects at 12 months than women assigned to follow the Zone, Ornish, or LEARN diets.[4] Therefore a low-carbohydrate, high-protein, high-fat diet, with good amounts of vegetables and fruit is in my opinion the best recommendation for weight loss. That being said the fats must be hormone free (rBST), and non synthetic. (I am not a full supporter of the Atkins diet because of its exclusion in certain phases of all forms of carbohydrate including vegetables and fruit, and the other part is not addressing the kind of fats allowed that may or may not include synthetic fats and fats coming from animals treated with rBST. To be fair though the latter happened more than 2 decades after his initial publication of the Atkins Diet Revolution. I admire the gentleman immensely for breaking the ‘Fat Barrier’.)
My direct message to Anonymous: Do not count calories to lose weight but AVOID refined carbohydrates (refined sugars, flour, rice, potatoes, etc.). Feel free to have unlimited amounts of healthy oils and a minimum amount of protein (hormone free) of 80 grams per day. This can translate into eating 1-2 pieces of fried chicken daily or equivalent (as long as there are no mashed potatoes, breads, pasta, lasagna, etc.) and this should be amply sufficient for absorption of your vitamin D supplement. Additionally you may have unlimited amounts of vegetables and use fruit as your dessert. Please continue the exercise and target sleeping 7.5 to 8.5 hours per 24 hour cycle.
I do realize that the calorie count concept will be hard to get rid of but the science just isn’t in favor of limiting fats and protein. 
 Also an opinion of mine not yet proven: I fear low fat is more in favor of cancer evolution than not, unless the fat intake has come from animals treated with rBST. I fear the last will contain said hormone (in meats) or higher levels of insulin growth factors (in milk and its products) both which will encourage increase in cell size and number artificially. This seems to me to be dangerous ground to tread.
I hope this answers your questions. Stay the course of health, it is very very worth it.

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References:
[1] http://en.wikipedia.org/wiki/Food_energy
[2] http://www.merckmanuals.com/home/disorders_of_nutrition/overview_of_nutrition/calories.html
[3] GD Foster, HR Wyatt, JO Hill, AP Makris, DL Rosenbaum, C Brill et al (2010) Weight and Metabolic Outcomes After 2 Years on a Low-Carbohydrate Versus Low-Fat Diet. Annals of Internal Medicine 153: 147-157. Doi:10.1059/0003-4819-153-3-201008030-00005.
[4] CD Gardner, A Kiazand, S Alhassan, S Kim, RS Stafford, RR Balise et al (2007) Comparison of the Atkins, Zone, Ornish, and LEARN Diets for Change in Weight and Related Risk Factors Among Overweight Premenopausal Women: The A TO Z Weight Loss Study: A Randomized Trial. JAMA 297: 969-977. Doi:10.1001/jama.297.9.969.