I have read in the lotus-sutra that chanting the name of avalokitesvara can for example break sticks if one is about to get beaten. Are there recorded miracles that happened to people out there?
I don't think recorded miracles will help you much for even if there're detailed records, there'll always be 2 camps: the skeptics will always have their own explanation/interpretation while the believers will always believe it their way. So the best way is to practice and see it in your own experience. Check out Ven. Hsuan Hua's great commentary on the Lotus Sutra at http://www.cttbusa.org/dfs25/dfs25.asp . And per his explanation from the website, if one chants/recites half-heartedly simply for the sake of "testing it out", then s/he's gonna be disappointed.
At that time, the farmer did not remember that E shi yun was a line from the Great Compassion Mantra. After the man left, he remembered, "He is a Dharma Protector in the Great Compassion Mantra!" This is an inconceivable state manifest from the Great Compassion Mantra. But if you recite it just to test it out, E Shi Yun is not going to show up. It is only if you recite and believe in the Mantra that unlucky circumstances can be turned into lucky ones. If you run into E Shi Yun, be sure to recognize him. Do not be like the farmer who did not remember who he was until he was gone."