michael,
“Once someone has obtained samadhi (the observer, the act of observation, and the observed become a single unified whole), then samyama is practiced on different objects. So this means the practice of samadhi is turned to meditating on a part of the body, to achieve a specific power, or siddhi.”
Your statement is misleading. Because the way you have used the word “samadhi” here is simply concentration. And in fact, that is the meaning of the word amongst the Buddhists. Don’t become confused with this word, it has been used in various different ways. For the Buddhists, if you concentrate upon the breath, then you are performing samadhi upon the breath. If you concentrate upon a chakra, then you are performing samadhi upon the chakra. Wherever your attention is moving onto a single object, that is samadhi according to the Buddhists. But the word can mean something completely different if you are seeing it through different lenses. In most of the yogic sciences, it refers to different intensities of meditation which are bordering on the experience of awakening. According to this, there are various different kinds of samadhi. When all mental activity has ceased and you come to a direct vision into your true nature, it is nirvikalpa samadhi. If you are fluctuating between absolute stillness of the mind and activity of the mind, it is savikalpa samadhi. If you have come to integrate your awakening from moment to moment in such a way that this state of consciousness becomes as natural as one’s own breath, it is sahaja samadhi. And beyond this there are also other categories of “samadhi”.