Does my pet sync, and what do my buddies see?

Your pet, its name, hat, room, the hats and room items it has opened up, and keepsakes sync between your devices with Device Sync, a Supporter feature, using the option you choose in Settings → Device Sync: Cloud Sync, which also syncs between iPhone and Android, or iCloud (Google Drive on Android). They're included in WitnessWork Backup (Settings → Account) and in backups from Settings → Backup & Restore too. Its hearts aren't stored: each device works them out from your records. With Buddies, your pet's kind, coat, and name are shared (not its hat) with your buddies, end-to-end encrypted. To stop sharing them, turn off Pet in Buddies Settings; the switch shows once you have a pet. Nothing else about your pet, and none of your records, is shared.