I am following a 3 days per week workout schedule and I am seeing muscle and fat increase as well. I feel like I am eating too much since most of the time I am so full and feels like 'will all this stuff in my stomach get digested' and not hungry at all. I am planning to cut down on quantitiy of food, but too many articles online stress on never going tot he starvation mode (some even say it is all made up there is nothing like starvation/degeneration unless youa re really starving. Each website and forum posters looks like having their own theories formulated.) . My question is, if I eat just enough to keep me not hungry (all the time) can I keep the fat buildup to a minimum and not lose existing muscle?(In my opinion, I would consider my body's response more authentic than anything spit out by some caloric calculator) If you can point to any trust-able references ,that will be much appreciated.
As you said, there are several theories and it looks like most are supported by some facts or science. So in the end, my answer is no approach is effective for everybody. Just try it and check how does it work for you. We are not all equal and something that may work for you could not be effective on a different person.
Now to get more concrete, I did exactly what you are planning to do and it worked wonders to me. I lost four kilograms and kept my strength and lean mass. The result was that I was able to do 14 pull-ups, which I was never able to achieve before "dieting" like that.
Be sure to learn to distinguish between being hungry and just feeling like eating. Sometimes you may only actually be thirsty and need to feel your stomach with some nice water to stop the cravings.
Also, if you really like food as I do, prepare to be challenged, especially in the first days. Then your brain and body (but it's mostly the brain, actually) will become more acquainted to a smaller food intake.