I belive there are quite a few things that can be damaged, however there are not really any weapons (without hacking atleast) that are able to DO that damage. So it's not that important at the moment to know what can and can't be damaged.
The answer to most of your questions is "The game is in alpha, so it's super buggy" As for the third question I belive the red broken chain means you are having connection issues to the server.