1. Why should someone place blame on others when she herself has at some time been "blameworthy"? What gives a person the right to judge and ultimately blame others?
I take this question to be directed toward Scanlon. He would say that we have the "right" to judge and blame others because they are obligated to us by virtue of the relationships that we share with others. Being in a relationship (friendship, mentor, waitress, fellow human being) entails certain expectations. Because we enter into relationships, we make ourselves obligated to meet those expectations. When those expectations are violated, then the person has harmed the relationship. On the basis of harm to the relationship, we have a right to blame. It is not because we are morally superior that we can blame others. It is because we have entered into relationships with others that we can expect certain behaviors from them. When those expectations are violated, we have the right to alter our relationship with another person, which is just what blame is. Blame is to recognize a harm to a relationship and then alter the relationship accordingly.
2. What is the definition of "justice"? If two ideologies have different definitions of justice, how can we compare them?
"Justice" has meant a lot of things to a lot of people. Thrasymachus thought that 'might makes right' explains justice best. Rawls thinks that justice is fairness. We will see still more conceptions of justice in this section of the course. When different ideologies lead to conflicting definitions of justice, the philosopher's task is to ask which definition captures what justice really is. There are many relevant questions: What are the practical consequences of this definition? What foundational principles support this view? Is the view logically consistent? What other kinds of justification are present or lacking?
Ultimately, people may have different definitions of justice because they do not share basic values or they may prioritize values differently. For example, someone may value personal liberty more than fairness and equality. When this is the case, the best we can do is to identify the underlying reasons why we disagree and then talk about those differences, as well.
3. What would Rawls say about changing the "rules" of the game (life) during the game? Sometimes while behind the veil of ignorance, even if people decide on rules with the best intentions, the game may not be balanced?
First, it is right that in general, Rawls would think that it is unfair to decide on rules during the play of a game. This is because you already know what position you are in the game. As a result, you will be inclined to choose rules that are biased and in your favor. But yes, we can imagine that we are already playing a game the rules of which we must assess although we are already playing; this is exactly the situation we are in when it comes to the rules of society. We are already "playing". We are all already in society. So we must pretend as if we are not playing and try to set aside our personal interests and knowledge of where we stand in the game. We must put ourselves back behind the veil of ignorance and choose new, better rules.
4. In Rawl' "Veil if Ignorance" model of choosing just rules, what comes of the people who naturally take greater risks? A "natural gambler" might make decisions that could be self-serving even if the odds are against them.
You point out an important methodological point. Philosophy, political theory, economics and game theory all create models of human behavior based on the standard of a rational, self-serving individual. It does seem to be a problem that many humans neither rational nor self-serving. But remember that Rawls is not providing a description of how a society actually is modeled. He is telling us what how he thinks a society should be modeled.