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For price ceilings, does this graph mean the producers can set the price higher than P max but they can only sell at quantity Q1 which I think is contradict to the meaning of price ceiling?

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Ask me anything you like about chapter 2.3 Competitive Market Equilibrium

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In this graph for the producer surplus, if the producer said "we cannot decrease the price any further below than 5 dollars." Does this mean that the producer surplus triangle will be cut at the price 5 dollars?

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Does the price mechanism happen in steps (1. signaling, 2. incentive, 3. rationing, 4. perfect allocation of resources) ? or does each function happen individually? 

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Does the price mechanism happen in steps (1. signaling, 2. incentive, 3. rationing, 4. perfect allocation of resources) ? or does each function happen individually? 

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Can you please explain why consumer surplus rises even when there is an increase in price?

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Can you please explain why consumer surplus rises even when there is an increase in price?

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I thought DWL was just the lost revenue due to the taxation of the product but when I asked my Mom about it, she talked about how it had more to do with the collective loss of the producers and consumers as the consumers had to purchase at a higher price whilst the producers couldn't produce as much product.

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Is the consumer and producer surplus always equal when at equilibrium?