Dropping weight requires a caloric deficit, whether that is low or high carb doesn't matter.
However, macro-nutrient composition, and even type of food (nutrient-dense vs not) can have a major impact on satiety.
http://www.gnolls.org/2407/when-satiety-fails-why-are-we-hungry-part-4/ (The whole series is interesting.)
Many people experience greater satiation with meals higher in protein and fat from real food. This allows low carbers to naturally create a caloric deficit while imposing little willpower, making it seem easy. Others may still eat too many calories even if low carb. Some people feel more sated with some carbs.
Also, what works for a person with 25% body fat may not work well for the same person at 12% body fat.
Because of the wide range of experiences, it is best to give some different methods an honest try and see what works best for you (high/moderate/low carb, lots of fruit, less fruit, no fruit, dairy, no dairy, carb feeds based on activity, etc etc etc). Journals can be very helpful in this regard.
Basic ways of creating a calorie deficit:
- Constant 20% caloric reduction
- Intermittent Fasting but not making up for the lost meal calories
- Exercise/activities to increase caloric expenditure
- Combinations of the above
As you lose weight your BMR will go down (this is completely normal - a 300 lb man has a higher BMR than a 150 lb man). Be sure to figure out what you can eat at your new weight for maintenance or you will just gain it back.
If you are having a problem feeling hungry and your caloric deficit isn't ridiculous then try changing around macro-nutrients and food quality to see if it helps. Remember that habits take a little while to break - if you are used to eating breakfast and you try to fast through it, you will probably be hungry! You have to give yourself enough time to adapt to new things.
You are in medical "ketosis" when your body is producing some arbitrary number of ketones (I forgot the number offhand), but the ketotic state is a gradient, not an off/on switch. From a weight-loss perspective it's not a big deal whether you are in "deep" ketosis or "mild" ketosis. It's often useful if you have other conditions you are trying to clear up.
Also, it's good you made the distinction that it is body fat you are wanting to lose and not just body weight. Resistance training and eating adequate protein (1 gram of protein per lb of lean body weight would be enough) can help in this regard but I can't find my references.
I disagree with the notion that you need to "change it up" so that your body doesn't adapt (especially if it sounds like similar to "muscle confusion" ala p90x which is just marketing bull). You need to figure out how to work with your body and this often means learning what it is it's doing. There are good reasons to re-feed, carb cycle, etc. - it all depends on what you are doing, context matters.
Oh, and the last 5 - 10 lbs are usually the most difficult. There is good reason for this but this is already too long. Also, the above is mostly about weight-loss. If you have any conditions you want to try to remedy things get more complicated.