Just to be clear- The university that you study has the right to censor certain websites because they are providing you internet and hence they can stipulate the rules(for the service they are providing). However, the argument here is that the government should not block URLs because they are not providing the service and they are just regulators of this service. The argument here is that as regulators, they are going out of their purview by curbing on freedom of expression (guaranteed by the constitution).
Yes. If they do, what might happen is you might choose a different ISP. Its simply not in their business interest to censor content, hence they dont!
Typically, if they have to censor, it would have to be based on an agreement with the customer before hand, else it would be a violation of consumer rights!
When you join the unviersity you must have signed any terms of service. That usually includes statements like, internet from univ will be used only for academic purposes. This is why they block the websites