Indicator's value is updated every tick. In fact, it's tick-by-tick basis for everything including all predefined variables (Bid, Ask, Open, High, Low, Close, Vol) and all indicator's values. When price is changed, you'll get different values.
It should be noted that the start() is called on every new tick, and init() is called only once when you attach the EA to a chart.
Stop loss and take profit are executed on tick-by-tick basis too but at broker's side. Even you close metatrader or shut down pc, when price hits the SL/TP, broker will automatically close the order.