They said that nerves which damaged from vitamin b12 deficiency couldn't be cured, is this means that if anxiety or depression from vb12 is permanent?

The nerves that: are being referred to are neurons, physical structures that communicate throughout the body and need vitamin B 12 and other nutrients. The nerves you may be thinking of is a catch all term for anxiety. That is not a permanent condition resulting from low B 12. A mental health professional can help. Also see www.relaxationresponse.org Peace and good health.

Not necessarily: It's hard to find reliable information on this subject but I believe the nerve damage that's hard to heal is more the peripheral nerves than brain tissue. To treat neurological symptoms from B12 deficiency get the B12 level to at least 800 but also take a full B complex with the L-5MTHF form of folate (folic acid) & consider Fish Oil, Bacopa, Ashwagandha, American Ginseng, Acetyl-L-Carnitine and lipoic acid.