Does the Kyne's Peace shout work on everything, including mammoths, or are they limited to a certain level? What does higher levels of the shout do?
Kyne's Peace works on all animals except for Mammoths.
It has a maximum effective level of 20. Mammoths are level 38 according to the Prima Guide. The next highest level animals are Snow Bears, who are level 20, and are thus affected by the shout.
I've tested this against both, and those results seem to hold with no Illusion perks.
Haven't tested Illusion perks, but in theory they shouldn't change the result, as Hypnotic Gaze and Animage offer a combined +16 levels of effective targets, which would bring the maximum affected level to 36. Since Mammoths are level 38, they would remain unaffected.
According to UESP,
The only thing that changes with levels 2 and 3 of the shout are affected area and duration - it's the same maximum level of 20 at all 3 ranks.
It'd be interesting to see if Illusion perks enhanced it.