Can I create an iTunes U course indepedent of an educational institution?
You can inspect the agreements that Apple wishes you to accept as part of the enrollment into iTunes U as an instructor from the web page:


https://itunesu.itunes.apple.com/coursemanager/


You will need to sign in with an Apple ID or make a new Apple ID to access this page. It asks you to define your affiliation with some sort of school - so that might be a problem if you don't have a school that will permit you to represent them. You could of course form a school since the categories look broad (Kindergarten, Elementary, Middle, High School, Undergraduate, Graduate, Professional and/or Vocational) and it's not clear based on where you live what legal requirements are present to form a school.

There is a second registration step for each institution to establish a public iTunes U page that also might have more detailed requirements to vet the existence of a formal organization, but the footnote 3 on the main marketing page for iTunes U lists:


  Teachers not affiliated with schools that have public iTunes U sites are limited to 12 courses and 50 students per course.


So, you might either find a school that allows you to begin publishing or consider forming one. The system is clearly designed / worded to prevent just anyone from joining, but I don't know how strict Apple would be in approving an application. I'd say you wouldn't want to waste your time making a fictitious school or being dishonest on the application, but if you were unaffiliated, you might list that and see how the application process goes.