Can you actually die from black widow spider bite?

Rarely. The black widow is the most venomous spider in the U.S. People rarely die from a black widow spider bite, since the amount of venom injected is so small. However, there has been a recent report of a death associated with many bites: http://www.Dailymail.Co.Uk/news/article-2017600/man-dies-weeks-bitten-19-times-black-widow-spider.Html.
Yes. But this is extremely rare and (if happened) would occur likely only in the very young (infants), extremely old or individuals with other chronic illness.