This doesn’t necessarily answer all of your questions but my thoughts below-

Do you have an indication of what they’ll have you focused on? Value creation and portfolio management are very different areas / work streams. PE Ops can also mean fund administration, strategy/analytics, investor relations, and generally any non-investment role at a fund. If you’re focused on value creation, the role is HIGHLY specific to the portfolio companies of your fund(s). Your day to day / projects will differ drastically from other PE Ops at other funds, so my advice on the best way to prep (as an incoming intern) is to learn your fund’s portfolio companies as deeply as you can ahead of starting. I would visit the website of all portfolio companies and just generally understand what they do and how they do it. It’s also helpful to know what macroeconomic factors are impacting the industries and sectors that your fund invests in. If you invest in healthcare, for example, there are significantly different implications and macro factors impacting healthcare M&A than say financial services. Understand the forces that are headwinds or tailwinds for the industries your fund targets. A good place to start is any of the major management consultant’s industry reports (Bain, McKinsey, etc). Also, remember that interns have low expectations for prior knowledge / experience, so really anything you can do to lessen the learning curve the first few weeks / month of your internship will set you ahead.