Being a native Portuguese speaker I can say our lì (ali) and là (lá) won't sound right in some situations and I highly believe it's true in Italian as our language is also from Latin.
tl;dr: Qui and lì are determined, a precise point, qua and là is for generic indication.
Qui and qua are interchangeable in 99,99% of situations.
Lì and là are not that much interchangeable as là is better used when you can't point to the reference
Lí (pt: ali) is generally used when you can see the subject or a reference to the subject.
Là (pt: lá) is generally used when you cannot see the subject or a reference to the subject. Or when it's extremely far.
For example, someone asks where someone is and this person is at home, if the house is in vicinity you use lì, but if it's in the other side of the city you use là. If the person is abroad you would always use là, except if the country is really close, like you're in Torino and the person in Switzerland, if the person would be in France it would depend on where in France, if around Nice you can use lì, but if in Paris là.
I would not say
Lui è lì in Cina, unless I'm being sarcastic because someone asked if the guy is close or I have a world map and am pointing to China. (Pointing in a world map also applies to qui if your finger is really close)
In Portuguese we also have two versions of here as in Italian, though our version of qua (cá) is more restricted than Italian in Brazilian PT. Assuming it's the same as there I can see situations where a correct use would sound better.
Qui (pt: aqui) is better used for really close, like on your side or in the very near vicinity that you can see and would easily be able to call the person.
Qua (pt: cá) is for any close vicinity
Ex.: You are in a party and someone texts you asking for someone you went to the party with.
If the person is still with you, you answer with qui:
È qui nella festa
If the person is not with you any more, or you just know the person is in the party, the best answer is qua:
È qua nella festa