Why is server preventing admin styles? (Was: Where are WordPress sessions saved?)

WordPress doesn’t use sessions. User authentication is done with cookies. But, there are many plugins that use sessions for some purpose, and it is possible that you are using one (or even more) plugin that is using sessions. You should try to determine which plugin does that and start from there. Search for the session_start() function to find which plugin uses it. You need to either update the plugin or if the problem is not solved, to replace it or contact plugin author for help.

As for the issue with load-styles.php, it might go aways once you solve sessions problem first.