Does Foucault believe that prison can be abolished as a penalty?

No. Foucault's whole argument rests on the idea that prison is inevitable in modern society. Its abolition is unthinkable, partly because the practical alternatives simply do not exist, and partly because it is a central part of modern systems of power and discipline. Foucault's argument is that modern societies (he is thinking particularly of France) are based on the idea of individual liberty. As prison deprives people of their liberty, it is the most "obvious" penalty. More importantly, the systems of discipline and observation that operate within the prison extend outside its walls: the carceral system integrates the prison and the wider world. Foucault does not argue that the prison cannot be changed, however: the further development of the human sciences may lead to them taking over some of its functions. You should consider in relation to this question how far you think Foucault's idea of power and the discourse allows individuals to act freely and change things like prisons.

What is the prison's place in society?

This is a complex question, but the simple answer is that Foucault sees the prison as very closely linked with many of the structures of modern society. The mechanisms of discipline and power that control the prisoner's life also control that of the citizen. Foucault's account of the development of the prison and the carceral system makes it clear that society has a "carceral texture" and is penetrated by the same mechanisms that operate within the prison. Equally, through its construction of delinquency, the prison helps to control and regulate class conflict and popular illegality. You should recognize that the prison and society always operate together to produce these effects.

Why does Foucault call Discipline and Punish a history of the modern soul?

Essentially, because in order to explain why the prison became the major instrument of penality in Europe, he consider the structures and mechanisms by which people are disciplined. These mechanisms act upon the soul, rather than the body, and so in explaining how modern penality operates, Foucault also tackles the soul. Also, in writing a genealogy of punishment, Foucault in part asks us to look inside our own souls. The development of discourses that exclude people and brand them as abnormal reflect badly on those who are classified as "normal", a fact he feels we should consider. Discipline and Punish is not just a history of the modern soul, but also a critique.