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.

Plus with sound ! ^^

About 3) :  I think Lua is so easy by itself, you can pretty much look at what its syntax is and right away dive in Nspire Lua.

You can look at other's code, tutorials, documentation etc., it will really help you a lots

if that's true I am a bit worried
5 * 24 = 120 hours and i think i have 0,5 til 1 hour a day (maybe some more in weekend but still ) so it would take me 120 to 240 days to make a game like nyancat :O