"Equivalent device" for testing for NP and coNP?
I will not directly answer your questions, as this would result in explaining the definitions of $\mathsf{NP}$ and $\mathsf{coNP}$, which has been done before. However, using the following hint combined with the definition of the complexity classes indirectly answers your questions.



A modern computer with unlimited memory is equivalent to the concept of a register machine, which in turn is turing equivalent. Thus everything that can be computed on a modern computer with infinite memory can also be computed by a turing machine and vice-versa.


  A Turing Machine can't generate true (undeterministic) random numbers
  while on a computer you may use the noise of the microphone input...


A microphone, or any other hardware-based true random number generator, is an input of the computer. That means the values delivered by it are not computed by the computer itself. Note that you can also model random input by a two-tape turing machine, where one tape contains the random numbers.