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More importance can be attached to observations which are either of greater importance, accuracy (lesser variance).
All it means that there were more than one observations which had the same value.
The decimal point is used to show that the number is not whole. Numbers after the decimal point show fractions of the number so there is more accuracy.
No, to both questions.
No, there is never more than one median in a data set. The median is defined as the middle value when the data is arranged in order. If the data set has an odd number of observations, the median is the single middle value. If it has an even number of observations, the median is the average of the two middle values, which also results in a single value.