Is it ethical to approach a professor asking for a (unadvertised) postdoc position?
I think you are making a much bigger deal out of this than what it is. Ultimately, you seem to assume that this is something shady that should be avoided, as indicated by your word choices ("gray market", "should I give up and approach senior guys directly"). This is not the case. It is not more honorable to score a publicly announced job than to get one that has been offered to you personally and without lengthy official search.

Hence, the ethical implications over other postdocs are minimal to non-existant.


  One ethical concern that I see here is that in some situations even when the agreement between the professor and prospective candidate is made, the position still has to be advertised (e.g. this may be a legal obligation in some countries). The advertisement will attract a number of applications, none of which has a chance to succeed, since the deal about this position has already been bade behind the curtains.


This may or may not be true, but it is certainly not your ethical issue. This is a problem that the professor has to deal with.


  Is it true that when a candidate approaches a professor with a request like this, some serious ethical restrictions arise? Is it more difficult to turn the offer down, if you was the one who was asking for it? 


I don't see why this would be the case. A postdoc is a postdoc is a postdoc. You do not bind your soul to this professor for eternity because he has offered you a job directly. Generally, turning down offers may cause some -unwarranted- hard feelings (everybody involved is just a human, after all), but the same is also true for any other job search.


  Is it more difficult to terminate the postdoc contract earlier than expected (and move to permanent position, for example).


No professor should fault you for terminating a postdoc early to move on to a faculty position. Of course some will, but, again, this has little to do with how you got the job in the first place.

So if you have a network: go ahead and use it!