A biography, or simply bio, is a detailed description of a person's life. An autobiography is an account of a person's life written by that person. A memoir is a historical account or biography written from personal knowledge or special sources. An essay is a short piece of writing on a particular subject.
Breathing in the first sentence is a participle acting as an adjective.
The second sentence is an auxiliary verb. is and breathing make up the verb.
Breathing is ... go no further. Breathing is the subject of the third sentence. It can only be a noun or a pronoun when it is a subject. So here it is a gerund.