1. Poor (quality) education may stem from lack of government support/funding and regulations as well as lack of resources (financial, physical, human).
2. For legal requirements see the Constitution, 1997 Amendments to the Individuals With Disabilities Education Act (IDEA) or 1975 Education for All Handicapped Children Act (EAHCA).
3. Due process as regards grievance or administrative cases are pretty similar in any industry, the basic requirement is as follows: the person "charged" should be notified or receive a warning pertaining to the charges against him/her and should be provided the opportunity to air his/her concerns in an appropriate setting/hearing.
4. As regards professionalization of teachers teaching, are you inquiring about the standards for entry into the profession? That would depend on the country and the institution of learning.
5. As regards principles and teachers improvement, I'm not very clear on the question but I would think that this is dependent on the country and institution of learning. I work in the educational sector and we have faculty development programs aimed at helping our teachers improve themselves in relation to the courses they teach and for career advancement.
6. Accreditation is necessary for an educational institution to be permitted and recognized to teach certain things. The benefits (to name a few) are recognition, permission to teach, ability to acquire quality faculty (you can be choosy), SCU (school/college/university) may issue certain documents without passing through a higher body (ergo less red tape and paper work), receive perks such as subsidies and financial incentives. The legal basis I suppose is dependent on the country.
7. Quality Education is a vague concept. What is considered quality for one may be considered mal-education for another. It's not necessarily true that private schools receive more quality education than public schools. Quality education depends on the criteria set by the country/educational institution, but basically it should be providing correct information through appropriate mediums.