I wonder if someone could describe the similarities and differences between Motor execution and MI, MP and IM and more importantly, the one that is more correlated with motor execution.
I can start by saying that functional equivalence theories of MI defend that neurophysiological similarities of MI and ME justify making MI as similar as possible to ME. For instance, the PETTLEP model of MI, arguably the most influential model in sport psychology, defends that the more closely MI resemble ME, the more MI becomes an effective performance enhancing strategy.
For more on the PETTLEP model:
Holmes, P. S., & Collins, D. J. (2001). The PETTLEP approach to motor imagery: A functional equivalence model for sport psychology. Journal of Applied Sport Psychology, 13, 60–83.
I know this answers only a small part of your question, but I am not very familiar with MP or IM