Yes.
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Yes, you can if you have 3 of the same number. For example, 33, 33, 33. Your mean, median and mode will be 33 for all the them.
Mean, median, and mode are all equal in a normal distribution.
In a normal distribution the mean, median and mode are all the same value.
Yes.
They could all be the same number, e.g. 55555 (mean=median=mode=5) or they could be three numbers the same, with an equal space between the first two and the last two, e.g. 24446 (mean=median=mode=4). For the mode to be well-defined, some of the numbers have to be the same.