How do tuition and credit accounting work in an independent study course?
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.