widow is a woman whose spouse has died and a widower is a man whose spouse has died.
Wow interesting, when was the word widow first recorded in history?
Its terms are not applied to a divorcé(e) following the death of an ex-spouse
Does a woman whos second husband died after she the first one died have a special term for it?
term "widowhood" can be used for either  at least according to some dictionaries, but the word "widowerhood" is also listed in some dictionaries.
Are there any other characteristics expected of a woman when her husband dies?
Don't know what characteristics you suppose ,but.the word "viduity" is used occasionally