Everything sounds so simple until we try to explain it.

If the emulation is contained inside the universe being emulated, do you think the emulated universe includes the emulation contained within it? Does the emulation now contain another emulation? If so, now many emulations?

It's frankly not all that clear what this even means. When cosmologists talk about the "universe," the generally mean the observable universe, which is all events that have ever happened in the past light-cone of the observer. Since space is expanding, that is constantly changing, with the expectation being that at some point, from the perspective of anything in our current galactic supercluster, everything else will become causally disconnected when the expansion rate exceeds the speed of light and will no longer be in "our" observable universe, where even then it isn't clear what "our" means as it's also likely by then that black holes will be the only baryonic matter still in existence, and there will no longer be humans, life, planets, or even light most of the time.

As those black holes degrade via Hawking radiation over however many quadrillions of quadrillions of year, without gravitationally bound superstructures of any kind, eventually all fundamental particles will be causally disconnected from all others, permanently.

What then does it mean to "emulate the universe inside the universe itself?" How do you emulate a single fundamental particle with only a single fundamental particle? What is the distinction between the emulation and the real thing? The real thing has nothing else to interact with, so it can't compute. It's state can't be measured because there is nothing to measure with.

In short, I hesitate to speculate about what can and can't be done with the universe because what the universe even is will change quite drastically over long enough spans of time.

I don't think that's unhinged. One might think the emulation must contain a subset of the state variables of the universe. But if there are no state variables that problem goes away. I have reason to believe there are no state variables.

I don't think there's any reason you couldn't but the simulation might move so slowly that it's not useful.