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If all the members of a set are different values, there is no mode.
The mean, median, and mode are all measures of central tendency. For symmetrical distributions they all have the same value. For assymetrical distributions they have different values. The mean is the average and the mode is the most likely value.
A mean is an average (add up all the values and divide by the number of values). The mode is the most frequently appearing value.
You cannot. You have two choices - neither of which are particularly enlightening: If there are other values that could have appeared but did not, then each one of the observed values is a mode (they appeared more often than the ones that had zero appearances); or If there were no such vales, you have no modes.
I wouldn't, I would just say that there is no unique mode. While it is true that if all numbers have a frequency of 1 then every value is the mode, however this provides no analytical insight and thus it is pointless to say that all values are the mode. However it would be wise to note that if there is no mode then there is a uniform distribution which would indicate that all values are equally likely.