Are there any conditions that must be met for estimating probability when a fair die is rolled 20 times?
There are no conditions as such that must be met when estimating the probability of any event that occurs when a die is rolled 20 times. Each of the rolls is independent of the others and the number that shows up in any roll is not decided by the number that shows up when any other die is rolled.
There are many events for which the probability of the event taking place can be determined. Some examples could be the sum of the all the numbers that show up, the probability of any particluar number showing up, the probability of the number of times a particular number shoes up, etc.
You must assume that you have a fair die. (Or know the probabilities for each side if the die is "loaded").