There are several tests for probiotics, including resistance to stomach pH, resistance to incoming gastric juice and bile salts, non-hemolytic properties, antibiotic properties, etc.
No, there are specific criteria a bacterium must fulfill in order to be considered a probiotic. There are several good reviews on that; a fast search will easily lead you one of them.
Besides demonstrating their potential in vitro, as Minoo Moghimani summarized, you still need to prove that it is safe for the intended use, show that it had beneficial effects (cholesterol lowering activity, for instance) in at least 1 study in humans, and show that it remains viable in sufficient numbers in the product in which you included your bacterium. After passing through all these steps, you can finally call your "candidate probiotic" a "probiotic".
In relation to safety, bacteria for human consumption need to be in the Qualified Presumption of Safety (within the EU) and/or have GRAS status.