(A) The terms homogametic and heterogametic refer to the organism depending upon whether all the gametes contain one or the same type of sex chromosome (Homo = same) or two different types of sex chromosomes (Hetero = different).
$(i)$ Humans show $XX/XY$ type of sex determination,i.e.,females contain two copies of the $X$ chromosome and males contain one $X$ and one $Y$ chromosome.
$(ii)$ Therefore,ova produced by females contain the same sex chromosome,i.e.,$X$.
$(iii)$ On the other hand,the sperms contain two different types of chromosomes,i.e.,$50\%$ of sperms have $X$ and $50\%$ have $Y$ chromosome. Therefore,the sperms are different with respect to the composition of the sex chromosome. In humans,females are homogametic $(XX)$ and males are heterogametic $(XY)$.
Yes,there are examples where males are homogametic and females are heterogametic. In some birds,the mode of sex determination is denoted by $ZZ$ (males) and $ZW$ (females).
$(b)$ As a rule,the heterogametic organism determines the sex of the unborn child. In humans,since males are heterogametic,it is the father and not the mother who determines the sex of the child. In some animals like crocodiles,temperature plays a role in sex determination. Lower temperatures favor the hatching of female offspring,while higher temperatures lead to the hatching of male offspring.