Do native speakers of English think that I have only one friend if I say, "He is my friend."?
No. In that situation, a person would say, "He's the only friend I have."
"He's my only friend."
Remember, grammar books give single sentences with no context. People DO NOT spit out one sentence devoid any context. What are the two people talking about that he says that sentence:
Mary is referring to the fact that John was dying and needed a kidney transplant and Andy donated one of his. Mary further comments that his act was generous and selfless. Andy replies:
"He's my friend. I only gave him the kind of help he needed, one friend to another."