Some brief and not complete answers follow.

> I'm trying to get a grasp on exactly how many planes
> are defined in Unicode
> [...]
> How many planes are defined in Unicode 3.1?

There are 17 planes, and everything will be re-written to reflect that,  
eventually.  Most of the planes are empty (except for the non-characters).   
And two of the planes are full of user-defined private-use characters.

The ISO 10646 standard is being revised (or has been already?) so that  
Unicode and 10646 all agree on 17 planes.

Appendix C of Unicode 3.0 talks about planes.

> BTW, it doesn't make sense for every code position
> ending in FFFF or FFFE to be a non character.

Perhaps it doesn't.  But as I have said before, in other places:
"If everything made sense, we wouldn't need surrealism to explain it."

> 32 non character
> code values in the arabic presentation form block

Which are those?  Can you point to precise codepoint values?

> Why isn't the same rule applied to the hidden non
> characters, so that every code value ending in FDD0 to
> FDEF is also a non character? Is it to contribute to
> their hidden nature?

I don't understand this.  What is special about those codepoints?



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