does all the information on the Parent get copied to all of the Child tickets -----> No, but you can change the mapping to inherit more fields which are not inherited from parent to child... to do so you have to take a look and make sure the field you want to inherit from parent to child exists on HPD:IncidentProcessControl form and workflows which pushes record from HPD:Help Desk to HPD:IncidentProcessControl and from HPD:IncidentProcessControl to HPD:Help Desk have mapping for respective field.
parent and child tickets. How do they work? ----> as we know we have Original of and Child of relationship type in remedy so when a ticket is related which these types the child ticket will inherits fields from Original ticket(as stated in point1) and status will be Pending(Pending Original Incident). once parent ticket is resolved then child ticket will automatically gets resolved.