Your records are stored only on your device, and there is no cloud sync. On your old iPhone, open 設定 (Settings) → 備え (Backup) → 書き出す (Export), then send the file it creates to your new iPhone (via AirDrop, email, a file storage location, etc.). On your new iPhone, open 設定 (Settings) → 備え (Backup) → 読み込む (Import) to bring the records in.
No. Your records exist only on your device and we never receive them, so we are also unable to delete them for you. To erase them, use 設定 (Settings) → 削除 (Delete) → 全データを削除 (Delete all data) in the app, or delete the app from your device. Note that 全データを削除 (Delete all data) erases your records, fixed costs, and “no spending today” marks; your budget, colors, and display settings remain. To erase everything, including settings, delete the app from your device. Deleting the app also erases the records on your device, and they cannot be restored. If you need your records, export them from 備え (Backup) before deleting.
No. Your records are never sent to our servers either. For details, please see our Privacy Policy.
No. Oiko is a household budget book you fill in by hand. If you are moving from another budgeting app, you can import a CSV file that has date and amount columns (an Oiko+ feature).