It's like my wordpress dashboard has lost access to the world.

Hello everyone. I have researched a ton of information on the internet regarding my issues. When it seemed that I found the solution I was getting actually more confused. And now I’m totally stupefied by the amount of information and the lack of a real solution.

Ok, here is how it goes:

A while ago I noticed that my dashboard is changed and when I inspected it more closely I found these:

1. WordPress Blog roll-out is giving an error instead of normal entries:
“RSS Error: WP HTTP Error: connect() timed out!”

2. Other WordPress News roll-out is giving the same error:
“RSS Error: WP HTTP Error: connect() timed out!”

3. Plugins roll-out from the Dashboard is not showing anything.

4. Installed Plugins page is totally fine, but when I try to use Add New > Search and when I search for any plugin it shows this in a blank page:
“An unexpected error occurred. Something may be wrong with WordPress.org or this server’s configuration. If you continue to have problems, please try the support forums.”

5. Since all this happened one of my plugins (NextScript: Social Networks Auto Poster) has also gone nuts. It’s fine with posting the post to Facebook but It can’t do it for Twitter, gives me this type of error:
“Fatal error: Cannot use object of type WP_Error as array” or some other variation of the same error that says something about Array.

6. After some research, I turned the debugger on and it showed me this error:
“Notice: has_cap was called with an argument that is deprecated since version 2.0! Usage of user levels by plugins and themes is deprecated. Use roles and capabilities instead.”

7. Back in the time when I was receiving a comment on one of my posts on Facebook or Twitter it was automatically imported to my site via Disqus plugin, now this thing doesn’t happen.

I think these are all that I noticed.

I scanned the site for any malware or viruses, and it is crystal clear.
The site itself is perfectly fine and is also working perfectly fine, but the dashboard is nuts.

I’m having a headache already, can someone please try and help me with this? Will greatly appreciate.

Here is the site, but as I said no problems with it: http://www.epicshortfilms.com/