Do I have to put sunscreen on my body too?

If the sun is shining on skin other than your face, you need to apply sunscreen to those parts.
It will come off whenever you cleanse yourself.

Yes - sunscreen needed on exposed body parts.

It is better to apply sun cream to the exposed body parts. Not to whole body. Yes it is advisable to take shower to remove sun cream.

yes it is required to apply sunscreen to the exposed parts as if you apply sunscreen to your face only then your face remain the same and the other exposed areas of your body like neck and hands will get darken also cleanse it as it is must

Wear sunscreen not only on your face, but also on your neck (including the back of the neck) and hands. These are two places that show signs of aging the fastest! It's also a good idea to wear sunscreen on any bare body parts that will be exposed to the sun, such as your ears, lips, hairline, top of the head if bald, balding, or shaved, and top of your feet (especially if you want to avoid flip flop tan lines).