Yes, they do penetrate water. Some of the UV is reflected from the surface (about 30% I think), so just under the surface, there is about 70% as much UV intensity. As you go deeper, the rays get scattered, just as water can scatter normal light, and it gets darker the deeper you go. As long as you can still see light underwater, you are still getting hit by UV rays. If you are waist high in water, your upper body gets even more UV than if you were just standing in the sun, because not only do you get the rays directly from the sun, but you get hit by some of the ones that get reflected too!
I think I have already replied to this question!
Speaking of personal experience, I can guarantee you that sun’s rays penetrate water and that’s why you need to have suncream on also when you are in the sea.
However, different wavelenghts (different colours) can penetrate at different extent. For example, the blue wavelength can penetrate as far as 200 feet and this is why deep water looks like bluish,
Yes, ultraviolet (UV) irradiation (which is what makes you tan or burn) can penetrate the water. I’m not sure how far they can penetrate, but if you’re swimming outdoors you should make sure you have waterproof suncream on to stop your skin from burning.