No. Unopened canned goods can only be harmed if something damages the can, exposing the contents to air or, in the case of a food that would be harmed by freezing, if the can is kept in a freezing environment.
Yes, you can put a can in the refrigerator, although it is not suggested you put it in the freezer or the carbon-monoxide will escape, on top of the actual can expanding and WILL explode
You could, but it's not advisable. Moisture content from the compressor has to go somewhere - usually into the drip pan, but if that overflows, it's going to wind up in the carpet, which acts like a...