If "couldn’t" replace to "doesn’t", it will change the meaning?
Yes, it would change the meaning slightly if you said "doesn't care less". This is because "couldn't" forms a conditional tense, which implies a hypothetical situation. "Doesn't" on the other hand implies something more permanent. It expresses the meaning that someone "doesn't" care and never will care. "Doesn't care less" is also not really common to use, and the usual way to say this expression is "couldn't care less".