Did Alma keep learning the rest of his life? We know that he started teaching right away, but did he keep learning? In verse 35, we learn that Alma and the sons of Mosiah went about "explaining the prophecies and the scriptures to all who desired to hear them."
We have plenty of evidence that Alma knew the scriptures very well. John Hilton has done a lot of research recently on the topic of how Alma’s used Abinadi’s words. He found that when Alma was talking to his son Corianton, he used more than 15 phrases from Abinadi’s discourse.
Later, in Alma chapter 5, we can detect a lot of King Benjamin’s words and phrases in Alma’s great discourse in Zarahemla. What this tells us is that Alma had not only studied the scriptures, but he had internalized them to the extent that he could use their words and phrases and concepts seamlessly. He became deeply knowledgeable of the scriptures.
In addition, in Alma 40, we see that Alma knew about the different situations in the spirit realm, and the times of resurrection. In order to learn that, he had "inquired diligently of God that I might know—that is concerning the resurrection" (40:3). He did not consider that his conversion taught him all he needed to know. He kept seeking for further light and knowledge.
John Hilton III, "Textual Similarities in the Words of Abinadi and Alma’s Counsel to Corianton," BYU Studies Quarterly 51, no. 2 (2012): 39–60.