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InfluxDB
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Anything you put elsewhere is not more secure, unless you are more secure than Apple's servers, which seems highly unlikely. If you don't have it, it can't get compromised.
The user has an iCloud account, you can write to iCloud storage without making them "sign in" to your app. It's their data, they can find it in the folder for your app in their iCloud drive on a Mac.
And see https://developer.apple.com/game-center/ for a way to let two users coordinate "play", multiplayer, turn based, achievements, etc., which cover most of the interaction you'd need.
For sharing personality test, a person can do their own and their partner's, but for a better take on the partner you and your partner can each take your own test then generate a sharable fun code that captures the "bits" of the answers without repeating the test. As partners, you could tell each other the sharable code as a NFC bump or QR code to scan, or generate one of the word based codes like bitcoin wallet passwords.
See BIP39: https://github.com/bitcoin/bips/blob/master/bip-0039.
(This passphrase would be short if the test results distill down to a smaller set of outcomes, like 64 questions give 8 results. It would be long if you need all 64 questions' answers to match with.)