Compared to the more serious violations of TOS that cause users to permanently lose their accounts, inactivity is an easily solvable suspension that doesn't cause that. If you forget, then it'll be your reminder. If you don't want it at all, then invest in the better hosting packages such as...
PostgreSQL is not available in free hosting. It is available in the Illuminated and Premium hosting packages, though. Here's a plan comparison that gives more details on what is and isn't not available http://x10hosting.com/free-hosting-comparison.
If you were posting in order to stay active, then it wasn't necessary. All you had to do was login here and read the forums for updates and the like. This is the free hosting support section for anyone that has any problems with their account. Do you have a problem with your account?
You can change it to a different domain if you want. It's impossible to just delete it and nothing else because it's your main domain. Do you mean that you want to delete your whole hosting account altogether?
It shouldn't cause any problems that can't be solved either way. It's your choice to change your main domain again or to go ahead a register your co.cc for free.
Did you make an A record to point to your server? The cname should point to your server, not an x10hosting nameserver. At least, that's how I understand it through some brief research. Your server is boru with an IP of 69.175.121.66
Did you configure your addon domain correctly? It redirects to your root, but not your actual site. Try to fix where your addon domain is pointing to. Otherwise, remove it and then try again, or just change it to your main domain.