Assume following situtation.
I have made 5 public challenges, 5 games in each. Totally 5x5 = 25 games. But ONE person took ALL 25 games. I suppose it's little boring to play 25 games with ONE person. I offered him draws, but he didn't accept it.
How can I cancel/abort this games?
FAQ tells I can surrender on turn #2 without losing score, but it's lie.
If I wait until time expiration, HE will finish games and I will lose a lot of score.
Have you faced this problem? What should I do?

I think you are screwed since you posted the challenges and he accepted them. Since you now know this person will take advantage of your postings i would suggest that in the future you tailor the challenges to not include this person (you can pick what ranks you want to send challenges to). Also, why not just send out personal challenges, that way you will play the players you want to play. Also, if this person was of higher rank than you he would lose points on every game that is drawn so perhaps that is his reasoning for not accepting the draws.

Yea and verily.
By now this is a moot point, but here's two more cents.
If you are a new player, losing these games shouldn't hurt too much, especially if the greedy challenge accepter has a good rank.
(One to five games is a reasonable number of challenges)
Welcome to MAN
Have fun .

Is there really no way to avoid getting my public games taken by a particular person? I.e. some sort of personal blacklist?

I heavily prefer to issue public challenges, but there is a short list of people I'd really, really not want to play against.

I rarely issue public challenges anymore.
Sometimes I will accept a public challenge, but usually I send and receive persnl ones.
Also, getting involved in a tournament keeps the games coming.
There are a couple players I have a slight grudge against(for timing out a game they were losing).
Persnl challenges keep me from playing certain people or too many of the same player.
Have fun!