Best fitness vs mean fitness, initial range

1) Based on the example of Rastrigin's function. At the plot function, if I chose 'best fitness', on the same graph 'mean fitness' will also be plotted. I understand well about 'best fitness' whereby it plots the best function value in each generation versus iteration number. It will reach value zero after some times.

I don't understand about 'mean fitness'in the graph plotted. What do those 'mean fitness' values mean? How does the 'mean fitness' graph help to understand Rastrigin's function?

2) What are the meaning of the term initial population, initial score and initial range? I wish to have a better understanding of these terms.

3) The default value for initial range is [0,1]. Does it mean that 0 is the lower bound (lb) and 1 is the upper bound (ub)? Do these values interfere with the lb and ub values I set at the constraints?

4) I try to understand better about lb and ub. If my lb is 0 and ub is 5, does it mean that my final point values will be within 0 and 5?

5) If I know the lb and ub for my problem is between 0 and 5, do I just set the initial range as [0,5] at all times and may I assume that this is the best option for initial range, and I need not try it with any other values?