yes, they do pray to "satan" (the fallen angel), but only to placate him temporarily. i believe they have a gnostic conception of the world in that the temporal realm is the domain of the fallen angel....
The Middle East has an extraordinary wealth of schismatic and survivor religions. There are also the Jacobite and Nestorian Christians, the Mandaeans, and the Druze, as well as various peculiar Muslim sects, the Bahais, the Samaritan and Karaite Jews, and the "Mountain Jews" who are comparable to the Ethiopian Jews -- recognizably Jewish, but illiterate and out of touch with other Jews for centuries.
The Middle East has an extraordinary wealth of schismatic and survivor religions.
the key is *survivor*...there are just as many heterodox religious practices in south and east asia-but they do not organize themselves into such clear delineated entities because there is a much lower chance that the powers-that-be will declare them "idolaters" and remove toleration of their beliefs. the mountainous terrain + a hypercurious & often hostile majority faith (sunni islam) in much of the middle east means that minority religions have to organize, systematize and develop survival strategies. in contrast, in south or east asia, the minor sects & orders tended to blend into the major religious tradition and find a more ill-defined and flexibile place in the religious landscape.
The Yezidi are perceived as Satan worshippers, but it should be noted that newer religions often treat the deities of previous religions as demons. 'Satan', for instance, seems to be derived from the Egyptian deity Set, and the similar derivation of Beelzebub is obvious indeed.
An interesting story about the satanic worship of the Yezidis. Several years ago, I read, I think in the NY Review of Books, a story by a reporter traveling in Iraq who had heard the the Yezidis of a certain town worshipped 'the Evil One'. He happened to go to that town and entered the Yezidi shrine, where he found over the altar - a picture of Saddam Hussein.
I suspect the phenomenon you cite has a great deal to do with the very different nature of Eastern religions as compared to the three major (and multiple minor) religions that found their origins in the Middle East (an obvious point, I know).
It is worth noting that, if anything, Latin Christendom was far less tolerant of heterodox interpretations of Christianity (including some, and I suspect the Cathars fall into this category, that were more religions unto themselves rather than merely being deviant Christian sects). While it was possible for Druze and Alawites and Yezedis and Alevis to develop survival strategies, the various sects that developed in Christendom faced brutal repression and extinction.