Each year in August we publish a variety of Public Notices. A few examples of these notice requirements include procedures involving student records, non-discrimination, asbestos, board meetings schedules, alternative education, location of board policy books, and processes for comments and complaints. Where do I find the a "law" which specifically says we need to publish all these notices, and is it considered published if we just post them on our website? Or do we have to pay to run them in a print newspaper?
The posting requirements you identified are found not in just one law but in several different laws. A document outlining the various notice requirements is available at the Annual Notices link. While some of these require direct notice to parents, none of laws identifying posting requirements require the notices to be published in the newspaper.