The significance of the mean of a probability distribution is that it is the most probably thing to happen. The mean is the average of a set of values. If it is the average of a probability distribution, it is the most probable part.
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The mean of a discrete probability distribution is also called the Expected Value.
It is the set of values that a variable can take together with the probability or frequency distribution for those values.
It depends on the parameter - the mean of the distribution.
Nothing since it is impossible. No event can have 5 as the probability of success.
The mean and standard deviation do not, by themselves, provide enough information to calculate probability. You also need to know the distribution of the variable in question.