Can we prove what dates in history these texts were written?
Also, do we know exactly when the various Rabbis of these texts lived? What are those dates? Are there disputes about this?
Further, which historical records and artifacts are used to corroborate these dates? Are there any good books written on the topic?
There can be various practical applications for Jewish law if we know exactly when these texts were written. For example, if the Yerushalmi was written around the same time as the Bavli, then we may be able to rule like it against the Bavli, because Klal Yisrael didn't have a chance to disprove the Yerushalmi and make a final ruling whether the Bavli is the final word in halacha.