Are you running the latest stable version of WordPress (3.4.2?)
Your theme, Suffusion could be causing conflicts with a plugin(s). Maybe some of your plugins are really old, causing conflicts with WP and you should look for newer ones. Or your database is corrupt.
If you say that Twenty Eleven or Twenty Ten works with all the plugins okay then there is some conflict with your theme, Suffusion. If you're still having problems then it's a plugin or a combo of plugins or your database.
Have you tried asking at http://aquoid.com/forum/?
Another suggestion is, if you are running WordPress 3.4.2, upload all the core files that come with it to your server. Just overwrite the files that are already there. There is no reason to use ones you backed up because you shouldn't change any core files anyways.
Also try re-uploading all plugins fresh, again overwrite the ones on the server now.
You asked what was stored in your database. Think of it this way, anything you type, click on, save, edit, or create in the Dashboard is saved to the database. With the exception of uploading a file, that, of course, gets saved on the server. The database contains data in text form with all your settings, post text, which widget is active or not, your usernames, passwords, etc.
Hope that helps.