How to manage the relations between supervisor and institution?
You don't say what country you are in, and what instutional checks and balances exist is going to dependent on that. 

In the US, you will have a thesis committee that is (at least supposedly) indepedent of your supervisor, and, at least in theory, pulls rank on your supervisor when it comes to matters of your studies. In the UK there often isn't a committee, but almost all universities have a system of "second supervisors" or "academic advisors".

In both cases there will be almost always be a head of graduate school, or directory of graduate studies for the department, school or faculty, as well as a chair of the department/school/faulty. The head of studies nomianally out-ranks the supervisor, although politics can come into play here, but the chair of the department/head of school/vice-chancellor of the faculty genuinely does outrank the supervisor. 

Failure to progress (i.e. not doing well enough to continue your studies) is a disciplinary matter, and would be dealt with in a quasi-judical manner according the instututions rules and regulation. You will be able to find these online. 

In the UK there will be Student's Union, and perhaps even a Graduate Students Union who can represent you if you feel you have not been fairly treated by either your supervisor, your department or the university. I don't know how many US institutions have similar. In the UK you can ultimate complain to the government ombusdsman, the office for students.