You can't as said on the terms of service here
http://www.000webhost.com/includes/tos.php
Look at number 7
"7. We do not allow online gaming scripts such as ogame, mafia, etc.. (allowed if you upgrade account)"
Chat with our AI personalities
You need to have a upgraded account to have a Minecraft Server running on 000webhost.
no you can host your own server.
You have to be the host of the server.
If you are the host of the Server, you open up Minecraft Server . Wait for it to load then it will say its ready. If you are going to someone else's server, and it has no bars, then there server is not active. (Which means they dont have Minecraft Server up).
You do not need to own Minecraft to host servers for it.