WP’s & Doc in P6 is just a library of Work Products and Documents. It’s not a complete document tracking system but enables Projects players to keep inform of the status of the documents and can be assigned to WBS and Activities.

For standalone user – Public access is useless because it is only for network users.

For Network and or Web Access installation – Public access & Private access is meaningful.
The main idea is to have centralised document share server (network) where WP’s & Documents are save. Then P6 enable to create a link to those documents having a Public link access – where everyone on Project player can view the document including timesheet users and can limit the access using Private link access and security setting will apply.

Answers to your query:
1) Is it possible that all the WP docs created by me in one system can be opened in a new system or can I send my program to somebody else via email , where other user who is opening my program can also view all my Documents saved.
No! user are creating only link and not savings the documents and it won’t sent the attachment but if network share and have access to project whether timesheet user only can view the documents on Public access link.

2) we have an option called WP , what is the difference if clicked or unclicked this option:
The use of WP’s tick box is to identify the document is Activity output or Work Products. (i.e. Task is to draw a site layout then document is a Work Products)