The password is written to the Header of the Tape, so unless yo can directly access the tape, you must supply a password to access the data. I've forgotten which product it is, but one fellow found that a 3rd party pro duct that will extract individual mailboxes from a stores backup apparently does no header checking, and just scans the tape looking for an Exchange Backup. As a result his "secure" Exchange data was available without supplying a password!
If your security requirements are strict, you may want to look into getting an application that will encrypt the data as or before it is written to tape.
To your last question, Yes, since the password is in the tape header, as long as you know the password, the data is available on another system running BackupExec (as long the tape drives themselves are compatible, of course)