This paper extends our prior coherent MSDD Carrier Recovery system from QPSK to QAM operation and also characterizes for the first time the Carrier Frequency Offset (CFO) mitigation capabilities of the novel MSDD for QAM systems. We introduce and numerically investigate the performance of an improved MSDD carrier recovery system (differing from the one disclosed in our MSDD for QPSK prior paper), automatically adapting to the channel statistics for optimal phase-noise mitigation. Remarkably, we do not require a separate structure to estimate and mitigate CFO, but the same adaptive structure originally intended for phase noise mitigation is shown to also automatically provide frequency offset estimation and recovery functionality. The CFO capture range of our system is in principle infinite, whereas prior CFO mitigation systems have CFO capture ranges limited to a small a fraction of the baud-rate. When used for 16-QAM with coherent-grade lasers of 100 KHz linewidth, our MSDD system attains the best tradeoffs between performance and complexity, relative to other carrier recovery systems combining blind-phase-search with maximum likelihood detection. We also present additional MSDD phase-noise recovery system variants whereby substantially reduced complexity is traded off for slightly degraded performance. Our MSDD system is able to switch "on-the-fly" to various m-QAM constellation sizes, e.g. seamlessly transition between 16-QAM and QPSK, which may be useful for dynamically adaptive optical networks.