Does human brain produce nicotine?
No, the human brain does not produce nicotine. The brain has nicotinic acetylcholine receptors, but the endogenous agonist for these receptors is acetylcholine, not nicotine; they aren't named "nicotinic" because they are for nicotine but just because nicotine happens to act on them. Many other human receptors are named similarly, based on discovering the molecular basis for sensitivity to exogenous compounds.

The human LD50 for nicotine is reported between 0.5-13 mg/kg depending on age and other factors, but LD50 is only appropriate for evaluating acute toxins; many substances, including nicotine, are most often encountered in small chronic amounts, but concentrated availability of nicotine in insecticides or vape juice can be a plausible source for sufficient doses for acute toxicity. Studies of nicotine toxicity in relationship to smoking are going to be based on much smaller doses over many more administrations.