There is no prescribed timeline. You will graduate as soon as you complete the degree requirements. Most students finish in three regular semesters (e.g., fall, spring, fall, or spring, fall, spring) plus one summer. In the past, exceptionally well-prepared students have finished in two regular semesters; but this required a very careful planning of courses and also very hard work. Some students take four regular semesters or even longer, often because they are engaged in a significant project one way or another. Some students may take longer because they may have weak CS background and thus need to do background classes. In general, you should pace your study such that it provides the best balance between comfort and productivity.

Technically, you are allowed to take courses in other departments/programs. But be mindful of the usefulness of such courses. Non-CSE courses do not satisfy the graduation requirements in the Computer Science Department. There are some rare exceptions, however, where your project or thesis actually requires such a course to build up your background, But then this needs to be certified as such by your advisor. Your advisor will not certify just because you are merely interested in taking such a course. However, non-CSE grad courses (not undergrad) do satisfy the registration requirements for full-time students (12 credits for G1 and 9 credits for G2).

Regular courses are not typically offered in the summer. But if you are choosing Advanced Project or Thesis Options, summer is an excellent time to get some work done. You can register for CSE523/524 or CSE599 during the summer. You can also do CSE593 independent studies in summer.

No. Internship is not a requirement.

Yes. But there are several restrictions you will need to be aware of. As a graduate student you need to register for graduate credits. Undergraduate credits, for example, do not count towards full time registration. The department facilitates taking undergraduate classes as graduate credits via a course designator CSE 587, where the student takes a core undergraduate class and get graduate credit for CSE 587. But you will need to do additional work relative to an undergraduate student taking the same class. Plus, you will get fewer credit (2 instead of 3). Finally, such CSE 587 may not count towards MS graduation unless specifically approved by the Graduate Director. For more details, see the Graduate Handbook.

Yes, but this is neither routine nor automatic. Look at the graduate handbook for a detailed answer.

Similar answer as above. You will need to convince Professor Y first.

First convince a professor that appear to work in areas related to Topic X. Also, try to take courses related to Topic X to get to know the professors (and the professors to know you). Note that you will need the professor’s permission to register for independent study/project/thesis courses. 

This is usually a problem at the beginning of the semester as many students register for too many classes initially trying to make up their mind, but then they drop them when things start stabilizing. So, you will see most classes opening up in the late registration period. It is possible that some very popular classes do not open up. But again we are planning to offer some of these classes every semester. So, you can take this class in the next semester. If you are really interested in a class and that class is closed, good idea to show up in the first lecture anyway and speak with the professor. Sometimes professors can sign in students at their discretion. 

Please also note that we have recently seen very high demands for certain classes taught by certain professors. The department cannot guarantee that a student will be able to take specific classes in specific semesters. The department can only ensure that a student can graduate with an M.S. degree within three regular semesters (fall/spring) by satisfying all graduation requirements. If this is your third semester and a class you need to graduate is full and no alternative classes are available, please speak with the graduate secretary. 

Read the Graduate Handbook first to familiarize yourself with the requirements of the MS program. If you attend the orientation, this will makes things somewhat easier. If you miss the orientation, don’t panic. The orientation simply presents the Handbook and answers general questions. In the first semester, a good strategy is to take at least 2 breadth courses and at least 1 specialized course depending on your interests.