First of all, thank you all for the replies. I have kept those in mind and after receiving my Sigma 24mm 2.8, I tried to find out what the problem actually is. Although these might not be some new stuff for you, I wanted to share my findings here:
1- AF assistance works properly between f/2.8 and f/5.6 (or 8 the most). At 2 and 2.5, it is not reliable at all. This was the reason of back-focusing at times.
2- As the subject gets closer, it is more prone to front-focus. At around 2 meters and beyond, it is more consistent.
3- I expected the AF sensors to be smaller than the square on the viewfinder, but they are actually bigger. Somehow, strangely, right-upper side of my center AF point likes to work more and/or faster than the other areas. Also, even more strangely, that is the part which likes to be cheated and give false positives more.
4- Not exactly WB, but the light type has effects on it. In shadow, at home, however indirect sunlight it is, AF was more prone to fail than outside.
5- I have never used the beep, so I do not know how it reacts. But in the comparison of the green dot and the AF confirmation red square, I found red superior to green (well, saying this way, it sounded like Nikon is superior to Pentax
). The green dot has a much larger tolerance. Red square, though, is sometimes (or most of the times?) working only as a notifier of the green dot.
6- I realized that my eye got better as I tried to nail focus myself, and tested the system accordingly. More than half of the time I could find the correct focus when I was shooting close objects. Yet with the farther ones, my success level failed.
7- Lastly, AF is more precise depending on the distance between me and the subject and the side I am approaching the subject. If I am close, approaching from infinity and vice versa makes AF more precise and reliable. It is not scientific and just personal experience, though.
So thank you all for the answers again, they helped me!