1) Power estimates are provided in the usual Mplus output for Monte Carlo studies. For a general description, see e.g.
Muthén, L.K. & Muthén, B.O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling, 4, 599-620. Mplus inputs and outputs used in this paper can be viewed and/or downloaded from the Examples page. download paper contact first author show abstract
2) No, but it is easy to do your own Monte Carlo study in Mplus.