when we boill chicken/ meat in water, do the fat (majority of fat) goes out from them?

Answer 1

No and sometimes it makes the chicken tough by just boiling.
Baking in the oven, in my opinion removes more fat, taking the skin of removes moves fat and you can trim the fat on meat and chicken. Some fat is needed for a healthy diet.

Answer 2

Depends on how the chicken is prepared prior to boiling. If you take the skin (which has the most fat) off, then you've already gotten rid of the majority of the fat, but not all of it. Either way, skin on or skin off, when you boil a chicken, the foamy stuff at the top that you can skim off, is mostly fat. If you let the stock cool in the fridge over night, you'll see a layer of gel at the top, that too is fat. After you clean that off, you will have gotten the majority of the fat off the chicken.