Its a circle. Depression frequently leads to inactivity and overeating (for self nurturing) which then leads to gaining weight which leads to a poorer self-image which leads to depression and so on. Irritibility is a classic sign of depression.
Hmm. It could, but so could diabetes, heart disease, depression, or maybe the food is used to self medicate the mood problem such as temper in the first place. Or the person may be very bothered about their obesity, struggle with feeling of lack of control about the problem and are acting out. There are many components to obesity and its not just lacking will power or being lazy, see a doctor for help.
Indirectly it can. Excess caloric intake, especially rapidly absorbed sugars can stimulate Insulin activity that drives sugars to be absorbed into cells and storage. That can lead to low sugar in the blood and an irritated nervous system which needs a constant supply of sugar. A few hours after too much sugar you need more or you feel irritable and nervous. Healthier foods are absorbed less rapidly.