1) nspire Lua is Lua but with nspire framework functions in it (I mean it is not like the difference between TI-èBasic and Basic whom are really differents)
2) Yes. Personnally I learnt Lua while discovering and documenting Nspire Lua. But I'm not an example. On the other hand, learning a language is hard without a goal/project. Your goal : understand how Lua tables and meta tables work
3) You have the choice. So the question is "do you have time to learn completly Lua before learning the extra-functions of Nspire Lua ?" . If so, start open the huge Lua documentation
and read it from begin to end. Same for lua-user
documentation. Otherwise, use Inspired-Lua starting tutorials
4) What is a simple program for you ? For example I made in two days Nyan Cat
. Two days is really short I think and a normal person will make it in 5-6 days. Give an example of what you think to be a "simple" program/game.
sidenote : a string is a table of characters. 'a' is a character, "aaaaaaa" is a string. But "aaaaa \n aaaaaaaaaaa \n aaa" is also a string.