Is it permissible to drink water in a restaurant without knowing its exact price beforehand, and to be content with knowing it when paying the bill, given that asking about its price might cause embarrassment?

You are not required to know the price of every item in detail when purchasing; rather, you are obligated to pay the value of what you have taken or consumed. It is permissible to consume food and beverages before knowing their price or paying for them, as long as this is done with mutual consent and is customary. Imam Ahmad was asked about a man who sends to the grocer, taking item after item from him, and then settles the account. He replied: "I hope there is no harm in that." The apparent meaning of this is the validity of a sale where the price is agreed upon later. Your ignorance of the price of some parts of your purchases does not harm you if you know the total price, and this is not considered impermissible gharar (excessive uncertainty).