Well there's a good summary of RAID types here https://secure.wikimedia.org/wikipedia/en/wiki/RAID
, but basically it says you only need 4 active disks to keep a RAID 6 running.
You seem to have 15(?) total disks, with 2 Syncing and one Failed; just replace the Failed one and continue.
Obviously the less you use the raid, the faster the syncs will complete.
mdaddm --detail /dev/md3
Re space full:
when it's finished syncing, you need to do at least 1 of
1. purge some space
2. add more disks
3. backup and replace with something else