Nicotine can be fatal, but vaping it wouldn't be a way to do that. I buy it in a somewhat concentrated form of 10% nicotine, or 100mg/ml and dilute from there. A toxic dose is .6-1mg/kg bodyweight. That means the average 200lb person could die from as little as 54 mg of nicotine. That's 1/2 a ml of the concentrate I use and about 3-4ml of the average ready to use juice. That is also the amount of nicotine in 4-5 cigarettes. The reason vaping and smoking doesn't kill you is absorption ability. A cigarette releases about 10-12mg of nicotine, of which the body only absorbs about 1mg. Assuming similar absorption rates, it would be impossible to use enough liquid to reach that kind of concentration in the body before your body breaks down the nicotine through vaping. I think it may be possible if we skip the vaporizer and instead focus on nebulizing the liquid.
The stuffy nose is pretty common reaction to the pg in the liquid used. PG and VG are both potent humectants and can dehydrate you quite a bit on exhale. That 'smoke' is really fog, using water from your own body. Drinking extra water helps with this quite a bit. Also, some people are sensitive to pg and can get stuffy nose with it. I had huge stuffy nose issues when I quit cigarettes to vaping and learned the hydration thing quick. The stuffy nose thing seems to last just a week or two though.
Common nonlethal signs of nicotine overdose: increased metabolism, insomnia, nausea, vomiting, headaches, shortness of breath, heart palpitations, sweating and pale skin similar to a heart attack. Nicotine is a vasoconstrictor so I'm sure it probably can cause some short duration hypertension.
That said, it's also quite often prescribed by phyicians overseas as a weight loss product.