The second one actually shows an important concept.
If we -ignoring all the problems of computation, space, definitions themselves- can "simulate" our universe this would also include the simulator itself.
Best problem explanation for this forum is probably a StackOverflowException.
This came up already
Logically, you can't simulate the universe.
If you managed to make a simulator, then the universe would be different - it'd have the simulator in it. You'd have to simulate the universe with the simulator in it simulating the universe which had in it the simulator simulating the simulator simulating the universe... and so on ad infinitum...