If an 2005 sql express database has been upgraded to 2008 (it was attached on a machine with 2008) , is it still possible to use that same database on a different computer with with sql express 2005?
Definitely not. If you do need to go backwards, you'll have to use the Data Export Wizard.
No, the easiest to do is to use the wizards in Management Studio (under Tasks for a DB) and SCRIPT the entire database, making sure to specify compatibility with the earlier version. This will create a (probably huge) SQL script file which can be run on the SQL 2005 instance. It's probably more straightforward to update the other PC to SQL 2008 Express.
Almost certainly not.
Generally speaking restoring a database onto a newer version of SQL server works, and affected structures are altered as needed, but the same can not be done in reverse (newer versions do not support downgrading, and older ones would not know how to alter the newer backup file).
No. When you restore a database to a newer version of SQL Server (not including service packs and hotfixes), it updates the internal structure of the database files to match the structure used on the newer version. Once converted, there is no way to reverse it.