WD My Book Live Duo: Hard drive failure

If you’re going to answer your own questions, answer them correctly.  :)

  In case of failure of one of the hard drives. Can I access the data on the active hard drive?

In RAID1 mode (mirroring), yes, you can.  All you have to do is shut the box down, remove the bad drive, and power it back up.

Your data will continue to be available from the other disk, as if nothing were wrong.   That’s what RAID1 is supposed to do.

When you get the replacement drive, you shut the box down, install the new drive, and power it back up.   The RAID is then resynchronized to the new disk. 

In RAID0 (spanning) mode, NO.  If you lose a disk in RAID 0 mode, your data are irretrievably destroyed.