1. j is the component index; j = h for heptane and o for octane. You have to calculate P separately for each component. Pj is the vapour pressure of component j; Pc,j is (I'm assuming) the critical pressure of component j.
2. χj (on the LHS) is not mole fraction. It is defined for you. On the RHS, xj would appear to be mole fraction of j in the liquid, and yj the mole fraction in the vapour.
3. It is just a starting point. You are told to adjust T until yo + yh = 1.