Read the logs section of my signature, you should not be copying from the console, you should be uploading your debug.log to pastebin or Gist and supplying the link it gives you.
Fatally missing blocks and items tends to mean you are missing mods that the server has.
To help any further I would need your debug log (more info in my signature)
Keep in mind that unless you specifically set a launcher profile to use a separate working directory (where it will put the mods, logs, etc folders), it will use .minecraft which may have remnants from previous modded shenanigans.
Are you hoping it will show up by itself? That doesn't work with dedicated servers, even local ones.
If your client is on the same machine as the server, use "localhost" as the IP to connect to.