The Problem here is...
1) ... forget about calling Actionparts via Lua -- if you are looking for Lua-Equivalents, that is not what you want. (And yes, it can be a massive Red Herring.)
2) ... you ask a very vague Question, basically "how do I code?", and that cannot be answered simply. It would be more useful to know that you need something specific, so you can get Help for that particular Matter.
A Line you mentioned was sending a Character to a specific Position. The Lua-Equivalent would be this:
function SendCharToPos(CHAR,XPOS,YPOS)
getObject("Characters[" .. CHAR .. "]"):setValue( VCharacterDestination , { x = XPOS , y = YPOS } )
end
Then you would call the Function in another Script somewhere else (or in the same Script, possibly) by simply writing this:
SendCharToPos("CHARACTER_NAME",600,500)
I haven't tested the it, but I think it should work.
And if you want to send the Character to the Position of the Mouse-Cursor, the Line in Lua would look like this (taken straight out of a Script of mine):
getObject("Characters[INSERT_CHARACTER_NAME_HERE]"):setValue(VCharacterDestination, getCursorPos()
I hope that helps.
[EDIT: Pfft, now you got three different Versions of basically the same Instruction. But hey, different Lights to shine on one Spot, that is also helpful.]