Final answer:
The enzyme required to resolve a cointegrate structure is Transposase. For the impairment in joining Okazaki fragments, DNA ligase is most likely the mutated enzyme involved.
Step-by-step explanation:
The enzyme necessary to resolve the cointegrate structure is D) Transposase. This enzyme is involved in the process of DNA transposition, specifically cut-and-paste and replicative DNA transposition. In replicative transposition, transposase catalyzes the cleavage and strand transfer, resulting in a cointegrate structure. This structure is then resolved by recombinational mechanisms, leaving copies of the transposon at both the original and new insertion sites.
When looking at the impairment of Okazaki fragment joining at the replication fork, the most likely mutated enzyme would be C) DNA ligase. DNA ligase is responsible for the joining of Okazaki fragments during DNA replication on the lagging strand. If this enzyme is not functioning properly, these fragments cannot be covalently linked to form a continuous strand, leading to a disruption in DNA synthesis.