DNA Replication Enzymes - What do the following enzymes do in DNA replication?

Helicase:

Helicase is a class of enzymes vital to all living organisms. Their main function is to unzip an organism's genes. Helicases are often used to separate strands of a DNA double helix or a self-annealed RNA molecule using the energy from ATP hydrolysis, a process characterized by the breaking of hydrogen bonds between annealed nucleotide bases. 

They also function to remove nucleic acid-associated proteins and catalyse homologous DNA recombination. Metabolic processes of RNA such as translation, transcription, ribosome biogenesis, RNA splicing, RNA transport, RNA editing, and RNA degradation are all facilitated by helicases. Helicases move incrementally along one nucleic acid strand of the duplex with a directionality and processivity specific to each particular enzyme.

DNA Polymerase III:

Being the primary holoenzyme involved in replication activity, the DNA Polymerase III has proofreading capabilities that correct replication mistakes by means of exonuclease activity working 3'→5'(read in this direction). DNA Polymerase III is a component of the replisome, which is located at the replication fork.

DNA Polymerase I:

In the replication process, DNA Polymerase I removes the RNA primer (created by Primase) from the lagging strand and fills in the necessary nucleotides between the Okazaki fragments in 5' -> 3' direction, proofreading for mistakes as it goes.

It is a template-dependent enzyme - it only adds nucleotides that correctly base pair with an existing DNA strand acting as a template.

RNA Primase:

RNA Primase is a type of RNA polymerase, which creates an RNA primer. DNA polymerase uses the RNA primer to replicate ssDNA.

Primase catalyses the synthesis of a short RNA segment called a primer complementary to a ssDNA template. Primase is of key importance in DNA replication because no known DNA polymerases can initiate the synthesis of a DNA strand without an initial RNA primer.  

The RNA segments are first elongated by DNA polymerase and then synthesized by primase.

Ligase:

Ligase is an enzyme that can catalyse the joining of two large molecules by forming a new chemical bond, usually with accompanying hydrolysis of a small chemical group dependent to one of the larger molecules or the enzyme catalysing the linking together of two compounds, such as enzymes.