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!

I have no special experience in applying for or managing postdocs, but this is just my take on the ethics.

As regards your first question, I would say it is the professor who is being unethical if he arranges backdoor deals for postdocs, while still openly soliciting applications which he has no intention of considering. I don't see anything unethical about approaching a faculty member to ask if they have or will have postdoc positions available. If they don't want to give you special treatment, they can easily and fairly say something like, "Yes, we will be accepting applications in November, I'll forward you the job ad when it's ready." If they tell you you are a lock and then mislead other applicants, that is their issue, not yours. As an applicant, I can't see that you can be held ethically responsible for how other applicants are (or aren't) considered, since you have no real control over that process.

As for your second question, I think those issues shade from an ethical level down to the level of personal courtesy. My impression is that everyone applying for every job tells the offerer that they are really interested in it, even if privately they view it as only a backup option. I agree this is somewhat distasteful in that it's not totally honest and straightforward, but I don't see any way around it and I think everyone expects it. Unless you were down on your knees begging for the postdoc, I don't think people would consider it a real ethical breach for you to reject it.

Plus, it's easy to avoid getting in too deep by making your inquiry diplomatically: instead of saying "Hey I really really want to do a postdoc with you have you got one?" you can say "I'm looking into postdoc opportunities and your work looks very interesting, will there be any postdoc opportunities in your department/lab soon?" By mentioning opportunities, plural, you make it clear that this is only one of many options you're exploring, and you can avoid appearing to make a commitment at an early stage. There may come a later stage where they ask you for a handshake agreement that you will accept the offer when it is officially made, and if you reject it after such a handshake, that could be considered unethical, but at the early stage you're describing I don't think it would be an issue.

In the end, I think the questions about rejecting the offer or leaving the position early come down to personal and professional courtesy and the desire to maintain good relationships with these people. As a nonacademic analogy, imagine you call up your friend and say, "Do you want to go to the movies?" and he says "Yes" and then you say "Okay, you can go by yourself, I don't actually want to go, I was just asking." You may not be cited by any ethics board for that, but you will be perceived as a jerk. Likewise, if you string people along making them think you want a postdoc offer, and then cavalierly drop it, even if it's not an actionable ethical breach, you may gain a reputation as a sneaky and underhanded negotiator, which will not help your professional career.