Hey EirikAKAhagtorn,
There are a few reasons this could be happening. You mentioned you messed with some Noise Control settings. Try your FaceTime call with Voice Isolation activated. This will filter out background sounds and focus only on your voices. If both of you have it set, it will help keep your microphones from picking up other noises.
The issue also sounds like there could just be a delay in audio syncing for you and your caller. Check your internet connection and make sure you have a strong Wi-Fi or cellular network. If you haven't already, try a call on each to see if one is better than the other. Closing and re-opening FaceTime and restarting both of your devices may also help. It can resolve many errors that could be causing your delay.
Finally, consider whether your call has updated their software within the last few weeks. Apple just released updates for iOS, iPadOS, and macOS with some pretty significant FaceTime upgrades. If your caller has already updated, it's possible in the new update (like conversation awareness if they are using AirPods) is impacting your call. In this case, you might also consider updating to iOS 17.
Speaking of AirPods, test with a pair of headphones (if you haven't already) to see if it occurs when you use headphones.
Kindest Regards.