You can do

Random rand = new SecureRandom()
// 0 to 100 inclusive.
int number = rand.nextInt(101);

or

// 0 inclusive to 100 exclusive.
int number = rand.nextInt(100);

Note: this is more efficient than say (int) (rand.nexDouble() * 100) as nextDouble() needs to create at least 53-bits of randomness whereas nextInt(100) creates less than 7 bits.

Yes it is secure.

Code examination of java.util.Random shows that ints() creates a spliterator that uses internalNextInt(...) to generate the random integers. That in turn calls nextInt() on this. In the case of java.security.SecureRandom, nextInt() is overridden to generate a "secure" random number¹.

You can confirm this for yourself by looking at the source code.

^{1 - Of course, it doesn't actually make sense to call an integer or a sequence of integers "secure". And there are situations where SecureRandom may not have the properties that you require. (It depends on the actual RNG or PRNG implementation used by the class, the quality of the supplied seed or system provided entropy source, and so on.) But SecureRandom::ints() will generate a sequence of integers that has the same properties as if you made a sequence of SecureRandom::nextInt() calls on the same object. If the latter sequence is suitable for your purposes (whatever they are) then so is the former.}

Try using @PrepareForTest at the class level of your test, not at method level.

@RunWith(PowerMockRunner.class)
@PrepareForTest(SecureRandom.class) 
public class ExampleClassTest {
...
}

Edit: In order to invoke the mock, you need to do the following:

1) Add the ExampleClass to the PrepareForTest annotation:

@RunWith(PowerMockRunner.class)
@PrepareForTest({SecureRandom.class, ExampleClass.class}) 
public class ExampleClassTest {
...
}

2) Mock the constructor call for SecureRandom:

SecureRandom mockRandom = Mockito.mock(SecureRandom.class);
PowerMockito.whenNew(SecureRandom.class).withNoArguments().thenReturn(mockRandom);

A working example is given below:

@RunWith(PowerMockRunner.class)
@PrepareForTest({SecureRandom.class, ExampleClass.class})
public class ExampleClassTest {

    private ExampleClass example = new ExampleClass();

    @Test
    public void aTest() throws Exception {

        SecureRandom mockRandom = Mockito.mock(SecureRandom.class);
       PowerMockito.whenNew(SecureRandom.class).withNoArguments().thenReturn(mockRandom);
        Mockito.when(mockRandom.nextInt(Mockito.anyInt())).thenReturn(3, 0);
        example.method();
   }
}