Wtf, iron is all over the place. Diamond, though: it is a cause for celebration when you discover diamond. Just don't fall in some lava after you pick up the diamond.
I found them, I was so pleased with how many I found. Then there was a one-square hole just after a one-square drop. So basically a goddamn trap. There was lava below the hole :C
Well you don't really - unless someone has explicitly marked/reserved an area in a particular way, if it looks natural and isn't right next to something else, go ahead.
You could probably go so far as to say there is no ownership of space - nothing to stop you going and modifying someone else's stuff (though most people probably wouldn't like that, so best not to), but the game itself doesn't have a concept of ownership beyond personal inventories, so don't worry too much - we're not going to shout at you for making a mistake. :P
Although I will kill you if you trespass in my realm. :@