OK, so...
Is there a way to determine whether what we are experiencing is a reality or simply a simulation?
Maybe... but it depends on the extent of the simulation.
In effect, a complex enough quantum experiment could be devised where you could test the computational limits of an exterior (quantum) processing system.
However.... So you might end up with physics-breaking results from such an experiment, detectable (at a distance) frame-dragging, or ... the universe might conspire to hide such an experiments detectable flaws by shrouding any experiment with sufficient complexity inside a small enough confine behind an event horizon (i.e., any machine complex enough to run such an experiment might be so massive as to undergo gravitational collapse).
If the simulation were simple enough (with respect to computational power) then it might not be terribly difficult to detect.
What characteristics does reality possess that a simulation doesn't (or can't) possess?
A simulation should be bound by the computational limits of the processing system. So, loosely, if we think of this in terms of an increased number of qubits equating to the increased degree of quantum computing capability; one could argue (again, very loosely), that the simulation would only be able to compute sufficient complex interactions over a maximum amount of events, simultaneously.
However, given that actions that happen simultaneously are not, by definition, causally connected, it may not be necessary to process them simultaneously at all - or even in sequence.
A smart engineer building a simulation would probably come to the same conclusion and process event sequences "out-of-order," through a process called pipelining (in CS). You could further add in a superscalar architecture to your quantum computer allowing for greater simultaneous computational capability.
Inside the simulation, you could hide this from those living within the simulation by creating a time differential; such that, one clock cycle outside the simulation could be the equivalent to 100 inside the simulation. This would allow you to achieve an arbitrarily high multiple of computational power without needing a larger processing system -- just more memory to store data.
The effect for someone living inside such a simulation is that time for them would pass far slower than for someone outside the simulation.
What are the emergent properties of reality that do not (or cannot) manifest within a simulation?
If the simulation was a perfect quantum representation of our fundamental (and unified laws) of physics (which we don't have yet, as you know) then I don't think there are any. It should be near-perfect, if not perfect, again, within computational limits and assuming the universe can be completed described with quantum mechanics (I would assume it can be).
Can a theoretical simulation be designed that is absolutely indistinguishable from reality from every point within the simulation "superspace" such that only an observer not confined by the simulation would be able to tell if said "superspace" is real or simulated?
I would think so, however, if you're saying that someone inside the simulation could not, under any circumstances, detect they were in a simulation; then again, you'd need to refer to the aforementioned caveats.
If yes, then it would seem that Academic Skepticism (in the Classical sense) would be the only reasonable position to take with respect to knowledge. Literally everything would be "degrees of uncertainty". Even mathematics and "logic" could not be completely trusted.
I suppose that depends on how one philosophically defines "reality." Reality is very likely really subjective when we most often mean to use it in an objective sense. That isn't to say that objective reality doesn't exist -- it likely does; but it's rarely what we're referring to. IMHO.
