(a) As the separation of the two atoms increases, the attraction between them increases and tends to zero at infinite distance. This is sensible, since as two atoms approach each other from a large separation, their potential energy slowly drops as they are attracted together. Mathematically this is seen by the fact that both terms in the potential energy expression tend to zero as $r$ tends to infinity.
(c) As the separation of the atoms decreases further, the potential rises sharply, which indicates that it is highly unfavourable for the atoms to be squashed together further. This is seen in reality, where two neutral atoms do not increasingly approach each other indefinitely! Mathematically, this is the $\left(\frac{\sigma}{r}\right)^{12}$ dominating the other term, which leads to a very positive potential as $r$ decreases.
The $W(r)$ potential curve differs from the Lennard-Jones potential as it has a term to the power of $9$ as opposed to $12$. Consequently, the curve still tends to zero at infinity, still has a potential energy minima, and increases sharply with small $r$. Therefore it could well yield a good match with reality with appropriate values of the constants.