Cake Wallet is open source... you can verify the following yourself:
- Cake does not require an account.
- Cake provides nodes for convenience and, yes, they can track your IP and usage, which is why they advocate you point to your own node.
- For further privacy (IP obfuscation), TOR is fully supported and encouraged.
- For purchasing gift cards, only an email is needed as that's where the card is sent.
- Private keys are stored on the device and never shared... with anyone.
- Swaps are done through Trocador, a very popular service with an excellent reputation. Cake simply integrates their API.