Good questions. 1) Dragons need clicks as eggs, hatchlings (sometimes called hatchies) and mature hatchlings. As an adult, no. 2) Not as an adult. Eggs and hatchies can get sick and die, you can kill them (don't do that; abandon it if you don't want it.), or they might not get enough views. You see the fog clouds around two of my eggs? Do that when they are sick. You'll see a notice at the top of the page.
Clicked, welcome to Dragon Cave! Make sure you read up on what's rare, what's not, and how to get rares: http://dragcave.wikia.com/wiki/Which_egg_is_which?
Has anyone every attempted to get a Neglected Dragon? http://dragcave.wikia.com/wiki/Neglected_Dragon
Some new dragon eggs seem to have appeared, or at least ones that weren't (at the time) listed on the wiki. They appear to be rather common, but it's anyone's guess...
I use my computer a lot. :P I just happened to be one of the first people to nab one, and there should only be about 30 in existence at this point. *EDIT* Guess I didn't get the other new egg..
Now there's a ton of people looking to get one of those. The AP is packed... EDIT: Just got a Rancid one. Check it out!
