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>I would like to include sections of the Lua manual within my own
>documentation (especially the sections on variables,statements, and
>expressions).  As long as I cite the source, are their any usage
>restrictions in regards to copying sections of the manual?

No restrictions, expect the one stated in the copyright notice (which
applies to the documentation as well):

  The above copyright notice and this permission notice shall be
  included in all copies or substantial portions of the Software.

>What if I want
>to make a few changes to the above sections to simplify some things?

Same thing.

>In regards to naming, must I still name the scripting portion 'Lua', or
>since its a derivitive, can I name it more accordingly to the product I
>produce?

See http://www.lua.org/faq.html#1.7 .
--lhf