Trying to understand ceiling in supply and demand on picture I am having one problem, which I do not understand. Let's assume the government applies ceiling price below the equilibrium price. I colored it red in my graphs. 

Of course, supply would decrease, there would be a shortage. But why does everyone plot the supplier and consumer surplus as it is in the left picture?

Let's think about it. If the government says the new price is N dollars for something, this means that there are a lot more people who are willing to pay the N price. I just don't understand why we always plot it like those who are willing to pay the most will get it, since new N dollar price is now acceptable for many more people and they would grab for an item as fast as those who are willing to pay the most. What I am trying to say is, if there is a ceiling price for something, it's not affordable only for those who are willing to pay the most but by everyone who is willing to pay above the threshold of ceiling price. But I see no one plotting the model as I did on the right side of the picture. Could you please explain to me why?
This is due to not enough supply. So yes you are correct, more people can afford it now, but because the price is less, there is not enough supply for everyone, even if they can afford more than it cost.

It seems you are not taking into account dead weight loss.
Here is a link to help you understand it and use it.
https://corporatefinanceinstitute.com/resources/knowledge/economics/deadweight-loss/

An inefficiency occurs since at the price ceiling quantity supplied the marginal benefit exceeds the marginal cost. This inefficiency is equal to the deadweight welfare loss.

When it comes to rent ceilings, certain things almost always happen that make the people willing to pay more in order to get the product vs people willing to pay only the rent ceiling price. 

If a price ceiling is set, then there must be a way to assign who gets the low supply of the product. Of course, since there is a legal limit on the price, the price can't simply be raised. There are several ways this is done without raising the price: 

Black Market: For those lucky enough to get some of the short supply, they are often better off selling what they have obtained to the demanders that will get more benefit out of it. In some cities there have been ceilings put on the apartment rent. While the demand for apartments increases, the rent remains the same. When some renters are ready to move, they sublease their apartment instead of ending their contract. If they were renting for \$500, but someone who  is  willing  to  pay  \$1000, then the subleaser can continue paying \$500 and  pocket the extra \$500 he gets from the subleasee.