1. If a person's greatest fear is a boggart what will they see when they meet a boggart??
Possibly they would see a boggart in its true form? Or perhaps they fear a boggart becuase of what they already know it will become. In which case the boggart is not really thier greatest fear.
2. If a person is afraid of heights what does the boggart become??
Because this is an intangible fear, perhaps it will be up to the individual boggart to decide what to morph into. Hermione was afraid of failure, but beccause failure is an intangible thing, a boggart can't turn
into failure. So the boggart had to turn into something that could convey the
sense of failure, whilst maintaining the form of something different. I would assume that because the boggart had been living at the school, it would be familiar with many of the teachers and students. Because of this it knew that McGonagal was a powerful woman with enough authority that she could dish out failure. Quite a clever boggart.
In the case of hieghts, perhaps it would become a deep hole? Perhaps it could become a bird and carry the poor person out a window

3. If a person has claustrophobia (sp??) what does the boggart turn into??
Probably a closet that would snap its doors and attempt to swallow the person.
As for Moody seeing a boggart, maybe he is the first person to see it in its true form?
Maybe the boggart can sense if a person is seeing it, regardless of whether the boggart can actually see the person.