Are you getting this error on this page currently? The lines of code that are referenced in the error you first posted are not in this file. In the error you posted the line of code that was causing the error looked like this:
mysql_select_db($database_Connection, $Connection);
In the file you posted that line of code is not present, instead you have a select db that looks like this:
mysql_select_db($database_localhost, $localhost);
By the looks of your connection file it seems that the $localhost reference is the correct one. If you continue to have problems with this please also post back with a copy of any of the other DataAssist pages that are not giving you an error.