If you are using SQL 2008 enterprise edition or SQl2008R2 you may choose compressions for backups if you are not already doing that. that may reduce the backup file size.

yes, it is possible. In the backup task you have the option to specify multiple files for the backup. You might want to choose a separate backup task for each...

Backup the database using a job. If you backup the database files using the net backup they will not be of any use.

Can you login with some other admin account.

Can you see the table in the master database.