Ignoring everything else:
There are many types of radiation we already know of (Alpha, Beta, Gamma, UV, etc.), and having a not noticed one isn't really that hard.
Yes, it is that hard. Anything higher than a certain frequency threshold in the spectrum is already labeled as a gamma ray, anything lower than a certain frequency threshold in that spectrum is considered to be a radio wave.
I think of there existing a type of radiation sent out by celestial objects, and some types of radiation only works in direct contact, while others can pass through solid objects.
You're sort of right. Electromagnetic light is released by some such objects (mostly stars, but also from a few other interesting objects) in the forms of what we would call radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays. The statement that some of them only work in 'direct contact' is a bit garbled... but anyway, they do tend to possess some interesting qualities in 'passing through' objects. We use X-rays to check up our bones based on how they will go very easily through our soft tissues, but will get absorbed by various more solid tissues or most foreign objects; this causes the film placed behind a person to be developed in the areas where the X-rays were able to pass through, but not in the other areas, leaving a pretty picture of whatever was being looked at. Gamma rays in the same situation would pass straight through the bone and keep on going. Radio waves are helpful in underwater communications because ones of the lower frequencies can be used to communicate despite all the water in the way, but carry so little energy (and thus information) that you can't really send much of a message.
These also contain a LOT of energy, if absorbed. 'unknown magical' Radiation is fun, but only the Magical kind.
Depends. If a gamma ray were to pass through you, it would release a lot of energy, yes, which would tend to destabalize whatever it was near. The scary thing about waves nearing that frequency is that they can pass straight through your bones and there could be issues with your internal organs, which are important. All UV light can really do is give you a sunburn, and maybe skin cancer, since it doesn't have the penetrative power. For all the talk about microwaves being used as crowd control devices and how terrible that is, they could only act on an extremely thin outer layer of the skin and heat that up... the problem for the crowds being controlled, of course, is that that's where a number of nerve cells happen to be, so it's rather painful even if it doesn't really cause any physical harm. I'd say the radiation from visible light is pretty great, since I couldn't see without it.