Can a advance stage PhD student (without thesis subission) apply for post docs, or have to wait until the completion of final defence? I am interested to know, whether an advance stage PhD student (without thesis submission) can apply for post doc positions or not?
For postdocs that are publicly advertised, read the advertisement.  Typically it will say something like "Candidate must have completed PhD before starting date MM-DD-YYYY."  That means you can apply before you are finished, but your application will have to convince them that you will be done before MM-DD-YYYY. If you're offered the job but then don't finish your degree on time, you may lose the job.  (It is possible, but not guaranteed, that you could be given the option to delay your start until after you defend; or to be hired under a different title, usually with lower pay, until you defend.)

For postdocs that are not publicly advertised, where you have to contact the PI to express interest, your initial contact message can say something like "I am finishing my PhD at (name of school), working with (name of advisor), and I expect to defend in MM-YYYY."  If they respond positively, you'll know that's acceptable, and can go on with a full application if needed.