-black cats are known in folklore/old stories to be “witchy” or “bad luck”
-i’d say she was just passing by, but recognized the black cat or felt connected to it
-they have the same “reputation” as mentioned in first answer
-they might in another life
The two phases are called "Waxing crescent moon" and "Waning gibbous moon". During these two phases one can barely see the moon.