If air pollution is not controlled, it can/will cause many problems.
Yes it's correct.
Yes, "Examining the water and pollution levels" is a grammatically correct sentence fragment. It lacks a subject and a verb that would make it a complete sentence, but it conveys a clear idea about the action being taken regarding water and pollution. To make it a complete sentence, you could say, "We are examining the water and pollution levels."
this is the sentence I prepared for a math competition, hours spent on complicated math problems every day.
Controlled is spelled correctly.
"How are you" is a correct sentence.
Yes, this sentence is correct.
You are palpitating. This is a correct sentence.
With the exception of not capitalizing the 'y' at the start of the sentence, it is a correct sentence.
The Aztec empire controlled the Yukon Territory in Mexico. (Note: although grammatically correct, the Yukon Territory is nowhere near Mexico.)
That sentence is grammatically correct.
no it is not a correct sentence.
no_____If the sentence is You do do that (meaning You are in the habit of doing that) the grammar is perfectly correct and the sentence 'does have correct grammar'.