So, the latest buzzword in Bitcoin is manipulation. Has anyone worked out how much money and bitcoins is needed to trigger a change in the buy and sell behaviour of traders on exchanges?
No one can give you a precise answer as things get heavily complicated when you start to explore them in depth. There are many factors at play here which you simply can't consider in their entirety and interrelations. For example, when the price rises, there may be a tipping point somewhere on the price scale when any amount of coins sent into the orderbook will tip the scales in the downward direction, and then an avalanche of selling panic-orders will follow. And it is equally true when the price bottoms as even the smallest amount of new money can turn the trend in the opposite direction.
It is the same with the market sentiment, on a horizontal scale, so to speak. If it is strong and powerful (whatever direction), it would take plenty of money to turn in backwards. On the other hand, if there is uncertainty in the market and the trend is not established, small orders can easily change the direction where the price goes. As you can see, there cannot possibly be a simple and comprehensive answer to your question.