1) When was ISO 27001 standard published?
In October 2005, although a final draft version was published some months prior to this.
2) Is it related to ISO 27002/17799
Yes. It essentially described how to apply the controls defined within ISO 27002, and of course how to build and maintain and ISMS.
3) What is PDCA cycle of ISO 27001?
This standard for PLAN-DO-CHECK-ACT, and is a cycle described by ISO 27001 to enable continual improvement.