Have you had your breakfast? -- Is this good English?
"Had" is used to form the past perfect, as you describe above.
He had already left home without an umbrella when it started to rain.
But - "had" is also used as verb all on its own; it's not always a "helping verb."
As in "I have three cats," or "I am having breakfast."
So "I have had breakfast already" means "I have eaten." No past perfect.
[not a teacher]