(1) As was said earlier, your Disk Management is fine. It is normal for it not to show the secret MSR (Microsoft Reserved) partition. Yours is partition 1 on Disk 0. That pushes all the others up...
DISKPART> list part
Partition ### Type Size Offset
Partition 1 Reserved 128 MB 17 KB <<<MSR partition -- Disk 0, Partition 1
Partition 2 System 100 MB 129 MB <<<EFI -- Disk 0, Partition 2
Partition 3 Primary 930 GB 229 MB <<<Windows (C:)
Partition 4 Recovery 627 MB 930 GB <<<Recovery -- Disk 0. Partition 4
(2) You have proven your DVD will work properly when booted through the BIOS Boot Menu which is F8 for you. That is good. So, memorize how to do a /Import there (if/when necessary), which is...
DiskPart <<<Enter DiskPart
List Vol <<<List the volumes & their letters
Exit <<<Exit DiskPart
=== You should recognize the Windows volume by its label or size ===
=== Note its letter which may not be C: in this environment ===
=== Use that letter instead of X: in the following command ===
BCDEdit /Import X:\BU\BCD_Backup /Clean <<<Restore the backup BCD
Close the Command Prompt, & click "Continue" to return to Windows.
(3) You made a typo with...
BCDEdit /Set {fwbootmgr} Displayorder {bootmgr} /Addfirst
Instead of {bootmgr}, you entered a second {fw...}. I'm surprised there wasn't an error message. It did nothing. It did not add {bootmgr} to the top. Therefore, it never went to {bootmgr}. And that probably was a good thing, because you did enter the following correctly, but it didn't work (though it said it did)...
BCDEdit /Set {bootmgr} Device partition=\Device\HarddiskVolume2
Instead, it left the value at "unknown". So, it would have been a failed boot, (& you'd have had to do the /Import). But you did get the Path from the other command...
I don't know what to make of that. It's spooky. But let's try it booted to Windows at an Administrator Command Prompt...
Type "CMD" into Search, & click "Run as Administrator".
BCDEdit /Enum {bootmgr} <<<Show old {bootmgr}
BCDEdit /Set {bootmgr} Device partition=\Device\HarddiskVolume2
BCDEdit /Enum {bootmgr} <<<Show new {bootmgr}
If the Device is there & the Path is still there, then do this (otherwise don't do it)...
BCDEdit /Enum {fwbootmgr} <<<Show current {fwbootmgr}
BCDEdit /Set {fwbootmgr} Displayorder {bootmgr} /Addfirst
BCDEdit /Enum {fwbootmgr} <<<Show new {fwbootmgr}
That should add {bootmgr} to the top of the Displayorder list, meaning the next boot will go there. If all looks good, try the reboot. If it fails to boot, do the /Import using the DVD if necessary. (But if it gives you access to the internal recovery environment, use that.)
We may not need to do the /RebuildBCD. If this much works, we probably can fix your recovery environment entries in a similar manner using ReagentC. Then Shift+Restart will get you there.