Use Arrays.copyOfRange:

public static <T> T[] copyOfRange(T[] original,
                                  int from,
                                  int to)

Copies the specified range of the specified array into a new array. The initial index of the range (from) must lie between zero and original.length, inclusive. The value at original[from] is placed into the initial element of the copy (unless from == original.length or from == to). Values from subsequent elements in the original array are placed into subsequent elements in the copy. The final index of the range (to), which must be greater than or equal to from, may be greater than original.length, in which case null is placed in all elements of the copy whose index is greater than or equal to original.length - from. The length of the returned array will be to - from.

The resulting array is of exactly the same class as the original array.

In your case:

String[] grp = Arrays.copyOfRange(elements, i, i + n);

You could do it pretty much as described, first create a new array of the same length as names (since you want to keep all of the names, just rotate them). Next, copy every name with an offset of one from names to that second array. Finally, copy the first name to the last element in the second array (and print it). Like,

String[] names = { "Jeremy", "Aude", "David" };
String[] names2 = new String[names.length];
System.arraycopy(names, 1, names2, 0, names.length - 1);
names2[names2.length - 1] = names[0];
System.out.println(Arrays.toString(names2));

Outputs (as requested)

[Aude, David, Jeremy]

Java's Strings are immutable, meaning you can't change them. Instead, as @AshishSingh notes in the comments, you'll need to create a new String.

Just do this:

fruits[0] = manipulate(fruits[0]);

Here, manipulate() is your function which takes an input string, manipulates it however you want, and then returns the manipulated string.

public String manipulate(String oldStr) {
    StringBuilder newStr = new StringBuilder(oldStr);
    newStr.setChar(1, 'b')
    return newStr.toString();
}

I'm using StringBuilder which is a mutable object, so can have elements reassigned. I set the second character to 'b' and then return the new String.