Logs are stored on Mibbit's servers so you can access/search them from any computer as long as you are logged into your account. Viewing your logs and/or downloading is pretty much beta at the moment. Downloading too many lines (as .zip file) results in a server error (work in progress). See also http://blog.mibbit.com/?p=911
You must be logged onto the main client and have the preference enabled for logging to occur. Logs are private; we don't access them or give them to other people.
The Timestamp shown in the logs is based on the GMT timezone, and not your own. There are no preferences to change this.