Is there a need to destroy char * = "string" or char * = new char[6]?

No. You only need to manually free strings when you manually allocate the memory yourself using the malloc function (in C) or the new operator (in C++). If you do not use malloc or new, then the char* or string will be created on the stack or as a compile-time constant.

No. When you say:

const char* c = "Hello World!";

You are assigning c to a "pre-existing" string constant which is NOT the same as:

char* c = new char[6];

Only in the latter case are you allocating memory on the heap. So you'd call delete when you're done.

I assume when I do char* = "string" its the same thing as char* = new char[6].

No. What the first one does is create a constant. Modifying it is undefined behaviour. But to answer your question; no, you don't have to destroy them. And just a note, always use std::string whenever possible.