Specialists do move the market. The specialist is paid for each 100sh they move. If they can move the price into an area of with a high density of stop orders the orders will trigger and they make money. The specialist is one of the few who know exactly where those stop orders lie. Usually it is just above the prior high or just below the prior low.
re gaps: don't forget the rest of the world trades stock indexes too and the open of the US markets can (yes I know its shocking ) be gapped by moves in Europe. a typical scenario might be post-close US news which is moderately bullish but when Europe opens the follow through just isn't there and the stocks that were supposed to be up in sympathy with the US news start to get sold off hard...so that when the US wakes up the bullish news has led to a gap down seemingly from nowhere... re Friday's rally: i'm no expert but my take on these kind of out-of- nowhere rallies is that they arise out of very small imbalances of supply and demand in the after a long consolidation. why? because during the consolidation shorter term traders get sucked into taking positions that don't go anywhere. so as the consolidation continues these traders have no reason to get out - the market needs to show them they are wrong by moving against them. all it needs is a small bit of other-timeframe buying (in this case) to tip the balance and once the losing short term traders begin to cover the rally sustains itself through that initial breakout phase...its basically a quiet day anyway so the buying pressure created by the short-covering offsets any "value" selling...after that the breakout-retracement traders lift it again for its second-phase push up....etc etc not that I have any more idea than anyone else...