Additionally, could they capture white settlers?

I'll start with this question. Jemison (and variations thereof) is a common Seneca surname today because during French-and-Indian War, Mary Jemison was captured and adopted by two Seneca sisters. For a while she lived on the Ohio River with these women, but by the time of the American Revolution she was on the Gennesee River in New York. Like so many Seneca, she was forced to flee her home and faced starvation in the wilderness when the Sullivan expedition razed the villages in throughout the region. She has a pseudo-autobiography called Narrative of the Life of Mrs. Mary Jemison, which was dictated to James Seaver who is known to have been at least some edits to the content. Still work checking out. Incidentally, when she was captured there was a boy with her that was also adopted by another family.

What was a "Mourning War"?

Proper "mourning wars" are an Iroquoian tradition dating to the pre-contact era and immediately after. By the mid-1600s, they'd largely been replaced with a different form of warfare - though some have argued that the Beaver Wars of the latter half of the 17th Century are mourning wars writ large.

A mourning war is initiated by someone's sudden death. The grieving clan organizes a small raiding party (usually composed of the husband's of the clan, who belong to different clans themselves and aren't currently mourning the death of one their own). If the death can be attributed to a specific nation, that nation is targeted. Otherwise any enemy nation will do. The warriors go out, intent on capturing at least one individual from the offending nation to either face justice for the death or to take the place of the recently deceased. Killing isn't the objective, but it if occurs there is no love lost and it may suffice if no captives are taken. For the rest of this post, I'll quote another I wrote some time ago about what happens once the captive is taken: