Count heads across the stopping rule before setting a fair fee

Two coins are tossed. If they show different faces, the game stops. If they show the same face, both are tossed again together with another coin, and the game stops after that round. X is the total number of heads obtained throughout the game.

(i) Show that $P(X=2)=1/8$.

(ii) Tabulate the probability distribution of X.

(iii) A player pays k dollars to play and receives one dollar for each head obtained. Find k for a fair game.