I just started my second read of the series and right off the bat, I noticed at the end of the prologue, the two stories at the end from the fourth age. If those are from the fourth age, could they be talking about the aftermath of last battle in Rand's age?

No, the first one is clearly about the Breaking of the World at the beginning of the Third Age right after the death of Lews Therin, and the second one is clearly about the birth of Rand on Dragonmount.

 

They are from the Fourth Age describing the events at the beginning of the Third Age.

 

We'll probably get Fourth Age descriptions of the Last Battle in AMoL.