Now for the questions. In actuality, the reactions is almost irrelevant in the answer. Instead, evaluate the ideas they give:
In the above example, they say that the reaction is not spontaneous under standard conditions. However, when we lower the temperature, it becomes spontaneous. Think about this mathematically. In the second line, they say that as the temperately goes to 0, the reaction becomes spontaneous. So if we realize that ΔG has to be negative in this situation (spontaneous) and that the TΔS = 0 as T -> 0, we see that the relationship becomes (-) value of ΔG = ΔH. What this is saying is that as entropy becomes useless and unimportant (->0) the ΔH is the only thing left and it is negative since ΔG is negative at these conditions.
Now for the next part. So as we increase the temperature, the entropy term becomes important. We know that ΔH is negative. At standard temperatures (higher T), the -TΔS must "overtake" the negative ΔH to make the ΔG positive aka the reaction non-spontaneous. Thus, the -TΔS term must be positive overall. Mathematically, with T always positive, we can work out that the ΔS is negative.
So this gives the general idea of the problem solving behind these questions. You need to think about what is happening as these values change and what must happen such that the ΔG becomes negative, positive. Now this can be very hard to get without practice.
Another idea is to grab a chart like that in study guides that lays out all the situations in general and how the variables all relate in the relation. That is more straightforward and likely easier.
Also, the equation may help justify ur answer, The above chem eqn is a redox reaction of a metal and nonmetal, which is generally exothermic. Further, the reactions says that the substances start from solid Al and gas Cl to become all solid substance. In this hand-waving argument, solids are more ordered than gases. To have a solid and gas substance go to all solid is going from a disordered state to an ordered state of all solid, which begs a negative change in entropy.