How do I read these equations and evaluate the couple reactions? I'm unsure as to how to look at them and identify whether it is a couple reaction or not? Is it okay if the first equation has negative entropy? shouldn't one of them be favourable and the other one non favourable? 

To check which combinations of reactions will give ∆G negative that will be the spontaneous reaction.

QuoteIs it okay if the first equation has negative entropy? shouldn't one of them be favourable and the other one non favourable?

Only ∆S will not decide whether the reaction is spontaneous or not. We need to consider ∆H also and combination of both factors are included in ∆G equation.
Like formation of ethyne
You need to divide first equation by half and add it in second equation to get the desired reaction of formation of ethyne. Same mathematical operations you will do it on ∆G values and then add them. Now check if final ∆G is negative or positive. If positive then then non spontaneous and coupling is not helping us and if negative then coupling will help in making it spontaneous.
In other options check adding these reactions are giving ∆G negative or not. If yes coupling is helping otherwise not.
Extraction of solid Cu from Cu₂S is feasible only if you couple both reactions.
Formation of N₂H₄ is non spontaneous in option 1 (∆G negative for first reaction which is formation reaction).Now if I couple it with any of other two reactions given still ∆G will be positive so this is the answer in which coupling is not making it spontaneous.
In all rest ∆G is negative on adding reactions.