While no one is raped, a character does push themselves on another, and the character who does not want to have sex is momentarily cornered. They do not end up having sex.
By our standards, the book depicts a lot of child abuse. Children are shocked with electricity, encouraged to behave sexually, and are even intentionally deprived of nutrients in the womb,
Almost everyone in this society is emotionally dependent on the fictional drug 'soma.' In particular, one woman who had been unable to take soma for years, takes so much soma that she is constantly under the influence and dies after a few weeks.
1) Near the end of chapter 6 (pages 90-91), some characters see the corpses of animals that were electrocuted by getting too close to an electric fence.
2) A dead dog is mentioned on page 96
The mother of one of the main characters gets lots of men to cheat on their husbands and doesn't understand that it's wrong. The whole culture is also very much hookup and no long term relationship oriented to the point that it is forced upon them.
Society is structured into castes using eugenics, where the lower castes are engineered to be less intelligent and given manual labor jobs. The higher castes look down on the lower castes. One caste of people, Episilons, are described as 'semi-morons.'
Most characters in the book hold the opinion that if you are not very sexually active you are considered strange and dangerous. This is expressed throughout the book.
Based on the nature of their orgies and the amount of clones that people have it is likely that at least once or twice incestuous relationships have happened/happen in their universe but it isn't a major plot element and it isn't downright stated.