The sum of the probabilities of all possible outcomes is 1.
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Sum of all probabilities is 1.
Yes but it is not possible to attach any interpretation to that. The addition of probabilities makes sense only if they are mutually exclusive outcomes of the same trial. If they are, then their sum cannot be greater than 1.
Not sure about only two requirements. I would say all of the following:there is a finite (or countably infinite) number of mutually exclusive outcomes possible,the probability of each outcome is a number between 0 and 1,the sum of the probabilities over all possible outcomes is 1.The Poisson distribution, for example, is countably infinite.
A probability distribution must have a well defined domain - that is, the set of possible outcomes.For each possible outcome, there must be a non-negative value associated - the probability of that outcome.The sum of the probabilities, over all possible outcomes, must be 1.