Windows 2008 R2 backup and restore
File level backup: Select only Exchange mailbox folder:
Status:Completed with warnings.

Error in rename of E01.log during backup: Error [0x80070002] The system cannot find the file specified.

Whole volume backup: Select whole D: drive where exchange mailbox folder is located.
VSS settings: VSS Full Backup
No error is recorded. The E01.log is backed up.
When you back up the full volume, you can add exclusions to exclude some folders or files from being backed up.
Restore a database to its original location
Exchange will dismount the database that is in the location, perform restore, and then mount the database. Any transaction logs that are created after the backup will be automatically replayed into the database.
Backup Mailbox Database: Telus
Get-MailboxDatabase -ID "Telus" -status | fl name,mounted,Last*
Name : telus
Mounted : True
LastFullBackup : 4/19/2011 10:09:58 AM
LastIncrementalBackup :
LastDifferentialBackup :
LastCopyBackup : 4/18/2011 2:00:42 PM

New-MailboxImportRequest -Mailbox "Telus1" -FilePath \\ex2\II\test.pst

Dismount-Database -ID Telus
When Telus database is online, the Telus.edb fails to recover.
Restore the data from the backup to the original location

Mount-Database -Identity Telus
The log files are automatically replayed into the database because when I access the mailbox, the newly imported data is there.
ESEUTIL /ML e01.log

the next log files generation is E01000002DF.

If the log files are lost, you can mount it with dataloss.
Mount-Database "telus" -AcceptDataLoss
Recovery Database--dial tone
Perform VSS Full Backup of Telus database without error.
Dismount-Database -ID Telus
New-MailboxDatabase -Name DB1 -EdbFilePath "D:\Dialtone\DB1.EDB" -Server EX1
get-mailbox -Database Telus | Set-Mailbox -Database DB1
Mount-Database -id DB1
The client's mailbox is empty.
Clients send and receive several messages.
Recover the data from backup to another folder d:\recover

D:\recover>eseutil.exe /mh telus.edb
Extensible Storage Engine Utilities for Microsoft(R) Exchange Server
Version 14.01
Copyright (C) Microsoft Corporation. All Rights Reserved.
Initiating FILE DUMP mode...
Database: telus.edb
DATABASE HEADER:
Checksum Information:
Expected Checksum: 0x16249511
Actual Checksum: 0x16249511
Fields:
File Type: Database
Checksum: 0x16249511
Format ulMagic: 0x89abcdef
Engine ulMagic: 0x89abcdef
Format ulVersion: 0x620,17
Engine ulVersion: 0x620,17
Created ulVersion: 0x620,17
DB Signature: Create time:04/18/2011 13:55:24 Rand:273179805 Computer:
cbDbPage: 32768
dbtime: 312770 (0x4c5c2)
State: Dirty Shutdown
Log Required: 749-749 (0x2ed-0x2ed)
Log Committed: 0-750 (0x0-0x2ee)
Log Recovering: 0 (0x0)
GenMax Creation: 04/19/2011 12:37:43
Shadowed: Yes
Last Objid: 151
Scrub Dbtime: 0 (0x0)
Scrub Date: 00/00/1900 00:00:00
Repair Count: 0
Repair Date: 00/00/1900 00:00:00
Old Repair Count: 0
Last Consistent: (0x2DD,530,110) 04/18/2011 15:11:48
Last Attach: (0x2DF,9,86) 04/18/2011 15:37:56
Last Detach: (0x0,0,0) 00/00/1900 00:00:00
Dbid: 1
Log Signature: Create time:04/18/2011 13:55:14 Rand:273139160 Computer:
OS Version: (6.1.7601 SP 1 NLS ffffffff.ffffffff)
Because the database state is Dirty Shutdown, we have to run ESEUTIL to replay any outstanding transactions that might exist in the transaction logs that have been restored.
D:\recover>eseutil.exe /r E01 /i /d

D:\recover>eseutil.exe /mh telus.edb
Extensible Storage Engine Utilities for Microsoft(R) Exchange Server
Version 14.01
Copyright (C) Microsoft Corporation. All Rights Reserved.
Initiating FILE DUMP mode...
Database: telus.edb
DATABASE HEADER:
Checksum Information:
Expected Checksum: 0x1211a85c
Actual Checksum: 0x1211a85c
Fields:
File Type: Database
Checksum: 0x1211a85c
Format ulMagic: 0x89abcdef
Engine ulMagic: 0x89abcdef
Format ulVersion: 0x620,17
Engine ulVersion: 0x620,17
Created ulVersion: 0x620,17
DB Signature: Create time:04/18/2011 13:55:24 Rand:273179805 Computer:
cbDbPage: 32768
dbtime: 317332 (0x4d794)
State: Clean Shutdown
Log Required: 0-0 (0x0-0x0)
Log Committed: 0-0 (0x0-0x0)
Log Recovering: 0 (0x0)
GenMax Creation: 00/00/1900 00:00:00
Shadowed: Yes
Last Objid: 181
Scrub Dbtime: 0 (0x0)
Scrub Date: 00/00/1900 00:00:00
Repair Count: 0
Repair Date: 00/00/1900 00:00:00
Old Repair Count: 0
Last Consistent: (0x2EF,8,1F) 04/19/2011 14:19:15
Last Attach: (0x2DF,9,86) 04/18/2011 15:37:56
Last Detach: (0x2EF,8,1F) 04/19/2011 14:19:15
Dbid: 1
Log Signature: Create time:04/18/2011 13:55:14 Rand:273139160 Computer:
OS Version: (6.1.7601 SP 1 NLS ffffffff.ffffffff)
New-MailboxDatabase -Name "Telus Recovery" -Server EX1 -Recovery -EdbFilePath "d:\recover\telus.edb" -LogFolderPath "d:\recover"
Mount-Database "Telus Recovery"
Get-MailboxStatistics -Database "Telus Recovery" | Select DisplayName,ItemCount | ft -autosize

Recover the data for all mailboxes discovered in the recovery database (Telus Recovery) and restore them into an online Database (DB1).
Get-Mailbox -Database "Telus" | Restore-mailbox -recoveryDatabase "Telus Recovery"
Dismount-Database -id "Telus Recovery"
Remove-MailboxDatabase -id "Telus Recovery" -Confirm:$false
New-MailboxRestoreRequest -SourceDatabase "Telus Recovery" -SourceStoreMailbox "Telus2" -TargetMailbox Telus2
get-MailboxRestoreRequest | Remove-MailboxRestoreRequest