Q: If thoughts arise from Consciousness, and Consciousness is the Absolute, AND we are all connected to the Absolute, why do we not all have the same thought simultaneously?
A: This is one of those many questions which confuse reality and appearance. The absolute reality is that there is ONLY Consciousness and, from that perspective you cannot say any more. At the level of empirical reality, there is clear duality – world, object, separate people etc. At this level, separate people have distinct thoughts, which are private. You cannot mix these two levels except to acknowledge that the empirical level is only an appearance (even though we believe it is real most of the time). As a crude metaphor, you might suppose that you take a lump of gold and make a ring and a bangle from it. If you drop the ring in some chemical and it is tarnished, you might ask why, since the ring and bangle are the same gold, does the bangle not become tarnished also. But this metaphor has its limitations!
You might enjoy reading the discussion at http://www.advaita.org.uk/discourses/teachers/mindreading_benjamin.htm. Benjamin asked a similar question here: Why can’t I read your thoughts?