From the errors it looks like an URL is missing "http://" somewhere. But this is probably completely unrelated to the slowdown. I see it's not your domain, maybe a wrong URL in the theme somewhere?

What is the server like?

From your post I gather that you don't have admin rights to the server, you might need to ask for sysadmin help... Can you see what database queries are running in the system? That's the first place I'd look. The size of the database tables? There was a error in the stats package at some point that produced huge stats tables. Can you see the "load" of the server?

If you have no way of monitoring the system, then it's a bit of shooting in the dark. You might try purginng the old logs, there is an admin setting to purge logs "older than N days".

Edit: I use "MySQL Administrator" (it's bundled in MySQL GUI Tools at dev.mysql.com) to check for the database issues. With it you can see if some of the tables are abnormally large. You can also monitor the running queries, if there are a lot of "locked" queries, then it means that they are waiting for some other queries to finish. These are usually log table writes, they have to wait for other writes to finish the update the indexes. (Don't know if PostgreSQL is more clever with this, probably...)

Ps. A nice looking site, I hope you get it going.