How do tuition and credit accounting work in an independent study course? I've been talking to one of my professors at a Master's program about enrolling in an independent study course under his supervision. 

(An independent study course is a course in which a student engages in guided study on some topic under the direction of a faculty member. Students formally enroll in such a course as part of a degree program, just as they would for a traditional course, and it appears in the students' transcripts, academic records, etc.)

However, it's not clear to me whether independent study courses work the same way as regular courses with respect to tuition and credit accounting:

Tuition: Am I expected to still pay tuition for independent studies? 

Credits: With traditional courses, there's typically some quantitative relationship between the number of credits a course is "worth" and the contact hours it involves. For example, a 4-credit course involves a certain amount of class time.

With independent study courses, where there are no fixed contact hours, is it common for institutions to have some expectation of how much time a student is supposed to spend on the course, per credit hour? For instance, that a 1-credit course expects about N hours a week from the student.
Since you ask about 1 or 2-credits, I'm assuming you're talking about doing an independent study course with the professor and not creating your own independent study track.

Independent studies (also called independent readings, directed research, tutorials, etc.) are essentially micro-classes of one or two students. You come up with your own reading lists, discussion topics, or projects -- subject to the approval of the professor. Whether to list it as 1 or 2 credit hours (or in my university 3 or 4 credit hours) is up to you. In general, you should plan on spending as much (or more) time in your independent study as you would with any other class.

From the registrar's perspective, it's just another class that you are taking. If you pay a flat fee for up to 5 classes a semester, then it can be one of those 5 classes. If you pay a fee for each credit-hour, then it would count as one of those paid credit hours.

I do independent readings with the undergraduate seniors, master's students, and PhD students when they come to me with topics that are of interest to me, but aren't in the regular course catalog. Since faculty do not get paid to teach independent study courses (we don't get any more money for doing this, nor do we get course releases for it), we're essentially do them out of the good of our hearts or because the topic is particularly of interest to us and/or we'd like the interaction with advanced students.