*you can really consider all of the above terms to be interchangeable.
Who writes these articles?
Experts in their fields. For education research, that likely means professors in higher ed, as well as researchers who have or currently work in government or schools.
How is the process for getting published in refereed journals different than elsewhere?
The peer-review process is one wherein an author submits their research paper to a group of their peers (identified by the journal as others who are researching similar questions as they are) and that group of peers evaluates the paper for importance, novelty (does it contribute something new and meaningful to the field?), accuracy and ethics. This is a double-blind process, so that no one knows who is writing or who is reviewing; this reduces chances for bias. Once the article is refereed, the author typically needs to make revisions before the work is published.
Why do they write in these journals and not in magazines or newspapers or in books?
The most rigorous research happens in these journals. Publishing in these journals assures that your research will be read and cited by experts within your field of study. This research is the most up to date - once research is published here, it can be referenced for a general audience in newspapers or magazines, or it may be referenced in a more comprehensive work, such as a book. Having an article published in a journal is prestigious and may be a factor in getting and keeping one's job at a university. No, authors do not get paid by these publications.
How do I access these journals?
These journals are very expensive to subscribe to. This university provides access to many, and will borrow from other libraries on your behalf so you have virtually complete access to scholarship. You can search within the databases I recommend and Google Scholar (but use the link to GS that I provide since it links with our subscriptions).