Like others commenting, I am not impressed with this question's answers even as multiple-choice questions go. Depending on how the question is interpreted, all 4 could be argued to be correct.
But only C is always true for a competitive inhibitor. The others are true for some competitive inhibitors, but not all.
What characterizes competitive inhibition (rather than non-competitive and uncompetitive inhibition) is binding at the active site of the enzyme. Nothing else need be true. An inhibitor that binds the active site regardless of how or why it binds there is considered a competitive inhibitor. The other two types of inhibition rely on binding to allosteric sites (binding sites other than the active site) that affect catalysis typically by altering the tertiary or quaternary structure of the enzyme.
An enzyme's active site is characterized by its shape (the space it occupies and does not occupy), and which amino acid functional groups project into that site in order to chemically interact with substrates as a part of the mechanism by which catalysis occurs.
In order to bind to the active site, the inhibitor may but does not have to interact with the amino acid site chains involved in catalysis. But they all must be capable of fitting into the site well enough to stick there, typically through multiple low strength interactions such as Van der Waals forces. Which means the molecule must have a shape that resembles the substrate enough to fit in its place. It must have "physical structure similar to the substrate" enough to do so. Occupancy of the site prevents the substrate from fitting into the site at all and/or interacting with mechanistically important amino acid side chains. Simple capacity to interact with mechanistically important amino acid side chains is not enough if it doesn't fit into the pocket of the active site as well.
And since the core definition of a competitive inhibitor is binding to the active site and nothing else, similar physical structure is the critical factor that must always be present. Thus, C is the answer.
But there are issues that can confuse making other answers seem correct even to someone who has a reasonably good understanding of competitive inhibition. First, for enzymes catalysing reactions reversibly (such as carbonic anhydrase which can either take CO2 and water and produce bicarbonate and hydrogen ions or take bicarbonate and hydrogen ions and produce CO2 and water), the products can be substrates so one could argue A is also correct. They probably discount it because the product of the forward reaction is the substrate of the reverse. Statement A about competitive inhibitors could only be considered true for reversible reactions, whereas statement C is always true for both reversible and nonreversible catalysts.
Second, as you observed, the primary way an inhibitor has "physical structure similar to the substrate" is because it is chemically similar to the substrate. But this is not the only way. In your example consider the case where one carboxyl group (COOH) of the succinate is replaced by a nitro group (NO2). The geometry and size of the nitro group is quite similar to the carboxyl group. Thus the physical structure is also quite similar despite the chemistry being dissimilar. 3-nitropropanoate inhibits this enzyme by binding at the active site and thus would be a competitive inhibitor of the enzyme.
So the reason C is the best answer is because it is the only statement that must always be true for an inhibitor to bind at an enzyme's active site.