Here are the answers to your questions.
1. Diploma courses are short term and are served as an either qualification for the graduation course or they stand alone for specific skill. In case of the degree course they are treated as graduation course. And those courses are mix of variety of skills. You can take degree course and then pursue the post graduation on the basis of the skills. Degree courses are also eligible for higher education. Diploma being a stand alone certification often not accepted for certain graduation and higher graduation degrees. You may also find that lot of universities don't consider diploma for admitting into the degree course.
2. Diploma courses can be recognized on state level basis or the university level basis. In case of state level diploma courses, those are treated as under-graduation courses. In case of the university level diploma then those are considered as graduate level or stand alone. AICTE, NAAC and other committees do approve the graduation level.
3. There are plenty of diploma courses on the level of the management and law. In case of management there is one popular diploma known as DBM. In case of law the course is known as diploma and intellectual properties. Like this there are many other diploma and courses for management and law.