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Proportion is the probability of a selected sample. probability is the true probability of all cases. If this is not what you are looking for then please specify.
A proportion is usually between 0 and 1. A probability is always between 0 and 1, inclusive; 0 being impossible and 1 being certain.
Yes.
The difference between "at least" and "at most" is not restricted to probability. The difference is simply one between the precise meaning of the phrases in every day English language.
None. The full name is the Probability Distribution Function (pdf).