Is “Cina” offensive in Malay too?
Nope, in Malay "Cina" is used to describe both country and race.
Do we always put "the" before US? Is that necessary?
In English, yes. :)
I have never used the word Tiongkok for China.. Only Cina.
Tiongkok is a Hokkien word for China. Well, the relationship between those two is feisty to say the least
Why not 'How is the relation between China and the United States'? Does it have to be 'relationship' in English?
Perhaps you need "relations" instead of "the relation", but this sounds rather formal.