Social media analyses using computational methods are becoming increasingly important, especially for crisis communication and social media monitoring. We seek to investigate the validity and utility of computationally analyzing communicative acts in social media crisis news comment discourses. We implement an applied act classifier for a novel online context by utilizing few-shot learning and a small manually annotated dataset. To illustrate the usefulness of analyzing communicative acts, we show that how people use acts in comments notably changes across the crisis timeline. In contrast to classic crisis research, early social media crisis responses in our study do not show a heightened use of acts oriented to discursive struggle only, but instead resolution oriented acts are most common at first. In further analysis, we show that computational analysis of acts can complement traditional content analyses to reveal more specific insights on the functions and goals of comments. Our study paves the way for more fine-grained approaches to understanding social media discourses and crisis responses, offering potential new tools for crisis management.