My simple question to you: Have you ever seen some "black light" coming out of your TV remote, or the microwave oven?
What you need to understand is : "Black" is not a color. In optics, black is the absence of a colour...and these are two different things which is exactly why you can't feel or see vacuum simply because vacuum is the "absence" of matter. Also, there is a difference between seeing and feeling. The two things must not be confused. UV light (as Dr Jh pointed out) is not in the visible spectrum for the human eye. This means that the electrons in the sensory pigments at the back of the retina cannot be excited by UV light in a way that can make our brain register the signal as a colour.
Yet, this doesn't mean that the light is getting reflected completely simply because it cannot excite the electrons in specific chemical pigments properly. A part of the light will get absorbed and will make the molecules in the eye vibrate and will hence heat up the portions of the eye and cause burn damage much the same as an intense beam of laser does in laser surgery. You'll only know it when your sensory pigments get totally damaged and you simply cannot see any more!
.Simply increasing the intensity will not change the properties of the light, it will only increase the number of photons hitting the eye per unit time. Light is seen by the eye because it can cause chemical changes in pigments. And whether or not a photon can cause a chemical change depends upon the electronic energy levels in the molecule being exposed, and the frequency of the photon, not the number of photons. So your question can be re-framed as : Is there a possibility that if I get an extremely powerful red laser and point it at a peice of white paper, the color of light reflected is blue rather than red?...or anything else other than red!?
Answer to your second question:
Two waves of different frequencies (however small the frequency difference be) can never completely cancel each other, though two waves of the same frequency but different phases can. This is exactly the reason why physicists find it difficult to perform interference experiments, because it is very difficult to find two light sources with exactly the same frequencies. As a result, they have to divide the beam change the phase of one part and then make them interfere rather than using two different sources altogether.
As a bonus, watch this YouTube Video where this guy builds an intense IR source focused to a thin beam effectively so strong that even though invisible to the eye completely, it can simply put things on fire in a jiffy, and imagine someone pointed it to your eye!! Your retina will burn before it can see and if it doesn't you wont know even whether the light is on or off because retina doesn't detect IR!
So, yes playing with intense EM sources beyond the visible spectrum is exceptionally dangerous mainly because they are invisible, so the person involved will not know till the eye is damaged.