In general, use break inside a while loop is considered a bad practice. You should have something like this

public static void main(String[] args) {

    Scanner input = new Scanner(System.in);

    int number;
    int minimum = 5;
    int maximum = 15;

    do{
        System.out.print("Enter a number between" + " " + minimum + " " + "and" + " " + maximum + ":" );
        number = input.nextInt();
        if (number < minimum || number > maximum) 
            System.out.print("Sorry, invalid");
    } while (number < minimum || number > maximum); 

}

The difference between a do-while and a while is when the comparison is done. With a do-while, you'll compare at the end and hence do at least one iteration.

Equivalent code for your example

do
{ 
    i++; 
    ++j;
    System.out.println( i * j );

}
while ((i < 10) && (j*j != 25));

is equivalent to:

i++; 
++j;
System.out.println( i * j );
while ((i < 10) && (j*j != 25)) {
    i++; 
    ++j;
    System.out.println( i * j );
}

General comprehension

A do-while loop is an exit controlled loop which means that it exits at the end. A while loop is an entry controlled loop which means that the condition is tested at the beginning and as a consequence, the code inside the loop might not even be executed.

do {
    <block>
} while (<condition>);

is equivalent to:

<block>
while (<condition>) {
    <block>
};

Use case

A typical use case for a do-while is the following: you ask the user something and you want do repeat the operation while the input is not correct.

do {
   // Ask something
} while (input is not correct);

In that case, you want to ask at least once and it's usually more elegant than using a while which would require either to duplicate code, or to add an extra condition or setting an arbitrary value to force entering the loop the first time.

At the opposite, while loops are much more commons and can easily replace a do-while (not all languages have both loops).

Because when you type a and hit Enter, then the in.read() method returns three characters - 'a', the character for carriage return \r and the character for line break ('\n'). (Note that the combination \r\n is considered as line-break under Windows).

Your program will have significantly different behavior if you run it under Linux or OSX, because line-breaking character(s) is specific to the OS you're running the program on. Under Linux, it will be \n, under OS X-9 it will be \r, for example.

As a work-around, you can read the whole line (by using a Scanner) and trim it, which will omit the line-breaking character (disregarding the OS type):

public static void main (String args[]) throws java.io.IOException {
      String line;
      Scanner sc = new Scanner(System.in);
      do {
          System.out.println("Please a key followed by ENTER:");
          line = sc.readLine().trim();
      } while (!"q".equals(line));
  }

No, it does not exist. What would be the point?

Consider

do {
  ...
} for (int j=0; j<2; j++);

1. j is not available inside the loop body

2. The loop condition says loop twice, but the loop will execute 3 times.

We can address the first point:

int j = 0;
do {
  ...
} for (; j<2; j++);

but the for loop is already emasculated. It still suffers from obscuring the number of times the loop runs. At this point you're better off with

int j = 0;
do {
  …
  j++;
} while (j<2); // or 3, depending on what you want

or even

int j = 0;
do {
  …
} while (++j<2);