Apply ITIL framework for an university.

Usually, things are other way around. Namely, when people discuss ITIL implementation, concern comes from smaller companies, they ask themselves whether ITIL is suitable for them. Not the big, large organizations.
So, yes ITIL is applicable in your situation.
From your description, I assume operational part (i.e. Service Operation stage of the service lifecycle) is of primary interest. This articles goes bit deeper into this topic
ITIL Service Operations – From development to maintenance without headaches https://advisera.com/20000academy/blog/2015/10/27/itil-service-operations-from-development-to-maintenance-without-headaches/
Which roles do you need for ITIL Service Operation? https://advisera.com/20000academy/blog/2015/06/16/which-roles-do-you-need-for-itil-service-operation/
Service Operation in ITIL https://advisera.com/20000academy/blog/2013/05/27/service-operation-itil/

Second part of your question - change management, related risks, costs...etc is in scope of ITIL and related processes. Here are few articles that can help:
5 benefits of ITIL Change Managemen t implementation https://advisera.com/20000academy/blog/2016/06/21/5-benefits-of-itil-change-management-implementation/
How to make your investment in ISO 20000/ITIL profitable https://advisera.com/20000academy/blog/2017/05/18/how-to-make-your-investment-in-iso-20000-itil-profitable/
How to measure Change Management efficiency according to ITIL https://advisera.com/20000academy/blog/2016/10/11/how-to-measure-change-management-efficiency-according-to-itil/
How ITIL can help reduce the gap between customers and the IT department https://advisera.com/20000academy/blog/2016/06/28/how-itil-can-help-reduce-the-gap-between-customers-and-the-it-department/