Sonkem, I think you have the right idea about the first question. I'll just restate it for the sake of restating things, if you don't mind.
People who are afraid of boggarts are probably so afraid of whatever the boggart will turn into that they don't want to think about it and place their fear on the boggart instead. The boggart probably knows better, and so will turn into the person's original fear, regardless.
I don't know about questions 2 & 3, but if a person were scared of heights or claustrophobic, I don't think that those would be their absolute greatest fears. For instance, I'm scared of heights, but my greatest fear is something quite different.
What would the boggart turn into for me? That's easy. My old piano teacher, who'd scream, throw things across the room, and fling my hands against the piano as if she were trying to make sure I could never play piano again. Evil woman.