How does DNA know when to replicate?

DNA transcription and Replication is a product of cells responding to a particular cue. a cue or signal may specifically target a cell of interest or groups of tissue as in the case during development.

Transcription is mediated by a slew of factors: Everything from Oxidation state, ATP/ADP/AMP ratio, NAD/NADH ratio, elevation of various substrates which in turn can lead to upregulation of particular enzymes, thus induce transcrption to begin the synthesis of these. Hormones and extracelular signaling molecules can also influence DNA Transcrption.

Ulitmately all signaling which mitigates DNA transcrption activate a series of proteins known as transcription factors. These are proteins which migrate to the nucleus or already exist their, recognize various regions of DNA to recruit a variety of other transcription factors and scaffolding proteins to promote the unraveling, and transcribing of genes of interest.

Replication is controlled through a series of responses, checks, and regulations from a family of transcrpiton factors, such as cyclin dependent kinases (CDK) which activate a series of other CDK enzymes responsible for instigating DNA replication/cellular reproduction. This is a tightly regulated proceess with many factors involved. It is the process that if faulted can lead to uncontrolled ceullar grwoth, leading to tumor genesis and possibly cancer.

This is a very broad topic and this was only meant to give a general overview of the process. Their are 100's if not 1000's of mechanisms under review.

In breif, cells are tightly regulated and can respond to a variety of signals to elicit a DNA transcription and replication reaction.

To answer your second question, I believe it's DNA helicase that "unzips" the strand.