This is a site where we try to help students understand a few questions with which they are struggling. We are not able to simply answer all of the questions in a homework assignment. Therefore, it is not possible to answer all of questions 2 through 8. In my answer, I will help you think about how to answer the hardest of these questions which are, in my mind, numbers 7 and 8.
First, let us think about the scholars in the House of Wisdom and how they were able to be united even though they were of different cultures. Have you ever been in a group whose members were all working towards the same goal? Perhaps you have been on a sports team or in a school play. In such situations where a group of people are all working for the same thing, do you think they tend to feel somewhat united? If you are on a sports team with people who are part of different cliques than you are part of, are you more likely to feel a bond with them because you share this common goal? In my experience, this is the case. You tend to feel united with people (even if they are different from you) when you are trying to accomplish something together. You feel that you all have something in common that unites you and sets you apart from other people. Thinking about this, could a similar thing have happened with the scholars in the House of Wisdom?
Second, let us look at the importance of cities in the advancement of Muslim culture. What is the main characteristic of cities? Aren't they places where a large number of people gather together? If you have a large number of people gathered together, it is more likely there will be enough people to engage in many kinds of cultural activities. Think about two high schools. One has about 200 students and the other has about 2000. Which of these is more likely to have a drama club? Which is more likely to have a photography club? I would think it would be the large high school. Imagine if 1% of the people were interested in photography at each school. At one school, that would mean there would be a club of only two people while at the other school the club could include 20 people. Wouldn’t the club be more likely to form at the larger school? Might the same be true of cities? Might they be places where enough people gather that they can engage in all sorts of cultural activities and thereby advance a culture?