Should one inform the wife of a deceased friend about his corruption, his secret travels away from her, and his intention to marry another woman, or would that be considered backbiting?

The fundamental principle is that one who has died should have their faults concealed, and they should only be mentioned in good terms, unless there is an overriding benefit. There is no benefit for this woman in knowing the abominable acts her husband committed or his attempts to marry another. On the contrary, this could cause her pure harm. Therefore, it is obligatory to conceal it and not inform her or anyone else about it, for whoever conceals a Muslim, Allah will conceal him.