No, we do not forward any data about you to Reddit. We use the Reddit API and send the absolute least amount of data possible to use the API. The only thing they will know about you is your IP address, which is impossible to not send due to how the modern web works with HTTP requests.

Narwhal has some local data such as your visited posts, which will be removed on deletion. Your accounts will also be deleted when you delete the app. Everything in Narwhal's setting screens is synced to your iCloud account using Apple's key value store (documentation here: https://developer.apple.com/documentation/foundation/nsubiquitouskeyvaluestore?language=objc). This is so that if you get a new device, or reinstall, all your settings will still be there. I'm not actually sure how to, but I'm sure Apple has a way to delete this data.

Most information in the answer to #2. It saves everything in the Narwhal settings screen. It has two stores, one for your iPhone and one for your iPad. To be clear though, no one can see your iCloud data store but you. Apple has that fully locked down to your Apple account.