You are completely correct, but I thought I'd elaborate a little. Lì is a specific "there" - where someone is pointing, for example, or a previously established place. Là is a more general "there"; the kind of "there" usually accompanied by a vague arm wave. It could be better translated as "yonder", if you don't mind sounding fairly odd.
The same applies to qui and qua - qui is a specific "here"; qua is more general. A room is qui; a city or country is qua.
we don't know, the la' refers to how far away the "there" is. Either li (with an accent i cannot do on keyboard) or la' depends on how far away it is. One of them is for things "over there" that you can see, the other is for things you can't. I can't remember which ones which though, sorry