For an example of a well-written peer-reviewed paper with proper APA citations and an excellent literature review, see Burnam et al. (2014): "Do adaptive perfectionism and self-determined motivation reduce academic procrastination?" This paper demonstrates high-quality academic writing, thorough literature review, and proper APA citation style.
It would be inappropriate to simply cherry pick claims and citations from Paper A (essentially using Paper A as a proxy literature review); it is fine to use Paper A as a nexus for research that you then cite independently (after reading it!) to build up your own history of a topic and make your own arguments in it. And it is perfectly appropriate to cite a paper you used as background but did not rely upon for in-text citations.