Are there certain qualities that animals need to be tamed? Let's say, for example, a quadrupedal omnivore with intelligence on par with Earth's ravens. It does exhibit opportunistic predatorial behavior. It lives on a planet identical to earth save for the environment which is a worldwide dustbowl. The creature is described as having a pack mentality and communicates using a muscular fin supported by cartilage spines on its head. The fin can be raised or lowered and flushed with blood in patterns. Could an animal like this be tamed by humans?
Any animal can be tamed given enough time, it's all a matter of how much effort it will require and how much time and resources are the tamers willing to spend. Consider that taming is just selective breeding, over the course of many generations you select behavioral and physical traits that make coexistence with the animal easier. Probably the biggest limit would indeed be how quick the species reproduce, with faster breeding animals being much easier to selectively breed than slow breeding species. The rest is less a matter of taming and more of training, which is where the innate characteristics of an animal are much more important, since you don't just need them to be able to live in captivity with ease but also to be able to perform a specific task or active function.