Final answer:
DNA Ligase is the enzyme required for repairing the phosphodiester backbone of DNA during molecular cloning, connecting DNA fragments during replication, and molecular cloning processes.
Step-by-step explanation:
The enzyme required for repairing the phosphodiester backbone of DNA during molecular cloning is DNA Ligase. DNA ligase is essential for connecting the Okazaki fragments on the lagging strand during DNA replication and is also used in molecular cloning to join the ends of DNA molecules together, particularly after the introduction of foreign DNA fragments into vector DNA. In contrast, DNA polymerase is involved in synthesizing new DNA strands by adding nucleotides to a primer, while helicase is the enzyme that unwinds and separates double-stranded DNA, and topoisomerase relieves the tension caused by unwinding.