Every organ in your body that utilizes LDL can synthesize it de novo. Some of the heaviest users, like your brain, literally can't get it from your serum LDL levels - they do not pass the blood brain barrier. It is all synthesized locally.

PKCS9 inhibitors and mendelian randomization studies show that people function just fine with <10 LDL-C. (Other comments I have made in here have links to all the relevant studies)

Googling for statin and aggression links I find a fairly small set of studies with fairly disparate outcomes.