Understanding gene transcription and mRNA-protein (mRNP) dynamics in single cells during development has been challenging. We report that zygotic microinjection of purified catalytically dead CRISPR-Cas13 (dCas13)-fluorescent proteins and modified guide (g)RNAs allows single- and dual-color tracking of developmentally expressed mRNAs in zebrafish embryos over 15 cell cycles without genetic manipulation. Using this approach, we uncover 1) non-synchronized de novo transcription between inter-alleles; 2) synchronized post-mitotic re-activation in pairs of alleles and daughter cells; 3) transcriptional memory as an extrinsic noise that contributes to synchronized post-mitotic re-activation; 4) rapid dCas13-engaged mRNP movement in the nucleus with a corralled and diffusive motion, but a wide varying range of rate-limiting mRNP export, which can be shortened by Alyref and Nxf1 overexpression. Altogether, this optimized dCas13-based toolkit enables robust spatial-temporal tracking of endogenous mRNAs and uncovers features of transcription and mRNP motion in a multicellular developmental organism.