a. This pedigree given in the question shows the recessive inheritance because most of the individuals that have red hair have parents without red hair.
If the presence of red hair is dominant, red hair must be present in all the generations and at least one of parents of red hair individual will have that trait. But this pedigree is not like that.
So, this trait is recessive.
b. In most populations, it is rare. In the first and second generations, only one individual has the red hair.
In the third generation, among twenty individuals six individuals are having red hair.
In the fourth generation, eight individuals are having red hair where more than thirty individuals are shown.
In the fifth generation, it seems to be little more, out of 11 individuals shown, 5 are having red hair.
In the second part of the pedigree:
In the first three generations, it was very rare. The fourth generation individuals are more affected and carriers than the normal ones; among the IV generation-11family people. After the mating between IV-11 and IV-12, the red hair allele is markedly reduced in the next generation.
Generally, in most of the populations, red hair allele is somewhat rare.