Is the given language decidable?
Yes, your understanding is right. 

The first part (about context-free languages which are decidable) is unneeded. To apply Rice, you only have to show that the property at hand only depends on $L(M)$ (which it does, trivially) and prove that the set is nontrivial. So the whole exercise bogs down to: exhibit $M$ satisfying the reduction property, and $M′$ not satisfying it. 

To prove/disprove reduction you may have to use the fact that the language $0^p1^{2p}$ is decidable, as you argued.