A: I'd like to give you a definitive yes or no, but the answer to both questions is not so simple. The practices you mention have come to represent the sine qua non of movement meditation. At first glance, there doesn't appear to be anything equivalent in the Abrahamic religions. I know of no standard Christian, Jewish, or Islamic movement meditations that truly resemble the Eastern versions in either style or content.
At second glance, there might be such disciplines in the West and Middle East after all. It depends on how we define the term "movement meditation." Consider that until we Westerners became interested in Eastern forms of meditation, we generally did not use this word to describe Western spiritual practice. We were more likely to refer to prayer or contemplation. But once "meditation" entered our vocabulary and experience from Asian philosophies and religions, we discovered it in Western traditions as well. For example, Jews and Christians who had experimented with Buddhism, Hinduism, and Taoism began to search for and unearth "lost" or hidden meditation methods in their own religions. Today, there is a groundswell of interest in the Jewish mystical meditations of Kabbalah.
If we broaden the definition to include moving in certain prescribed ways during prayer and ritual, then certainly Jews, Christians, and Muslims engage in movement meditation but don't necessarily call it by that name. For example, when Muslims engage in salat, or prayer service, they perform the rak'ahs (bowing cycles) with a combination of standing, bowing, prostration, and sitting postures in coordination with head, hand, arm, and foot gestures. Similarly, Jewish and Christian worship include a certain amount of movement in combination with prayer. Done mindfully, could it be called "movement meditation"? Maybe, maybe not.
From the outside, we may notice movement similarities. But internally, there are fundamental differences. Practitioners of t'ai-chi aren't worshipping anyone or anything; they're moving to attain a state of harmony, balance, and unity, within and without. Muslims, Christians, and Jews, on the other hand, are expressing submission, obedience, and devotion to God.
While the dervishes continue their ancient tradition, Christians and Jews around the country are simultaneously digging into the past for movement sources and creating contemporary practices. Followers of Creation Spirituality, founded by former Roman Catholic, now Episcopalian, priest Matthew Fox, engage in Techno Cosmic Masses, an ecumenical postmodern worship experience that includes ecstatic music and dance, among other elements. In the Jewish Renewal Movement, we can find combinations of simple movements, dance, yoga postures, and breathwork with Jewish chanting, prayer, and Kabbalistic meditations. Some practices include either yoga-like postures or t'ai-chi movements based on the shape of Hebrew letters.
Eastern movement meditation and Native American ritual opened the door for Westerners to try an approach that goes beyond reciting prayers. Western practices may not define movement meditations along the same lines, but by consciously involving the body through movement, they're enlivening spirituality in the West.