i want to know can we use array index value for string operation?
No, you cannot. A string is a string and has string methods etc, an array is an array and has array methods etc.
It might have been easier just to ask that question.
Why do you not want to use "built in" methods? They are built in so that you
can use them. Not using builtin methods leaves you with just using arithmetic and other operators and assigning the results to things but that's about it: a sort of leaf-falling-from-a-tree-in-a-forest-unobserved situation.
As regards the "null" character (do you mean zero?): this has nothing to do with the number of characters in a string in Java. That is, strings are not terminated in any special way.