IIRC these are usually required to only invest into super secure stock classes like government bonds - which actually was a problem on its own during the last years as most of the government bonds considered secure enough were ultra low or even negative (Germany!) yield, so the funds and endowments actually lost money due to inflation.
Not really, at least not for all of them. US college endowments, for example, invest into all sorts of things, from highly illiquid developing market investments to options, ventures and hedge funds.
A couple of times at MIT I saw an overview with a general allocation. I do not remember the details and was not particularly curious, but it certainly had "we can invest in whatever we need and want" flair. It got a >14% average annual investment return for the last 10 years, not something one could get with government bonds. You can look at the endowment reports of the Ivies; many publish some outlines every year.