Can a computer simulate itself as part of a simulated world?
No, a computer cannot perfectly simulate itself in addition to something else without violating basic information theory: there exist strings which are not compressible.

Here's the simplest possible proof: suppose the computer has a total of $N$ possible states, and suppose there is something outside of the computer in the universe, so the universe has at least $N+1$ possible distinct states.  With zero overhead, each state of the computer can correspond to a state of the universe, but since the universe has more states than the computer, some states of the universe will map to the same state of the computer, in which case the simulation will not be able to distinguish between them.