I believe my devices have been compromised. How can I fix this?

My suggestions are based on what has worked for me with different issues over the past year and also what I have learned. If you are not using security keys, order two ASAP and start using them with all services (including your Apple Id) that support them. Yubi is a popular key but it might be smart to purchase two different brands.

(1)On a clean device (or at an Apple store) get a device firmware update (DFU) for your devices.

(2) Activate your devices on a clean private network, not a public network.

(2a) Complete the activation process WITHOUT entering your apple id or phone number.

(3.) As-soon-as your device is registered on Apple’s network and before you enter your Apple Id, place your device in Lockdown mode and make any other changes to your settings to secure your device.

(3a) Do not use your Apple Id email address for anything else; only use it for your device.

(4) When you have signed back in to your Apple Id or have created a new one, turn off the setting that allows developers to ask for feedback. Then, if you get pop ups asking for feedback you will know they are not legitimate.

(5)In the Accessibility settings, turn off the shake to undo feature so if you receive that pop up, you will know it is not legitimate and not to answer it.

(6)If you don’t know if a pop up is legitimate and cant close the screen without answering the pop-up, force your phone to shut down. Some of the pop ups that I received that were not legitimate were app surveys, “undo”, and “are you sure” pop ups. I’m sure there are many others. When I first realized I was receiving too many pop-ups, I tested the legitimacy of one app survey pop up by answering the pop up and then lost control of my screen time settings and screen time passcode.

(7) Delete apps you do not need/use.

(8.) Sign into apps when you need them. Do not stay signed in to your apps 24/7.

(9)Turn on cellular data to an app when you need it. Do not keep cellular access on 24/7 for all of your apps.

(10) Turn off: wifi, bluetooth, and your router when you don’t need them.

(10a) Stay off public wifi and do not share your wifi.

(11)Smart TVs, internet of things, and cameras are easily hacked. Put them on a separate network.

(12) If you use an email address on your smart TV, create an email address just for your TV and streaming devices. Several months ago, our hacker changed the email address on the YouTube app on our TV. This post is already too long to explain, but he used the original email password in the new email address he created to let us know he had the password.

(13) Read up on home printer and router security. Home printers are an easy access point for hackers. Update your router firmware if it is not automatically updated. Replace routers that could be out of date. Disable remote management of your devices.

While every situation is different, you might have malware on your devices. A couple of days ago my screen time passcode that I knew was correct was not being recognized. I was already signed out of my apps. I use only cellular data and 4 apps had access to the cellular data. I turned off cellular data for my browser and my screen time passcode was accepted.

If you feel an unauthorized person/app is remotely using, controlling or monitoring your device, then that is possible only if you have done one or more of the following Don'ts...

1. Don't hand over an iPhone to kids or to a stranger without Enabling Guided Access
2. Don't share Apple IDs
3. Don't Jailbreak
4. Don't share sensitive information pertaining to your device
5. Don't give in to Phishing
6. Don't plug in your device in Airports and Public places through third-party cables and trust the device. Beware of Juice Jacking. (Especially in India)
7. Don't leave your iPhone unlocked and unattended in public places like offices, schools, malls, etc.

If one of the above is true then quickly change the Apple ID Password and Return iPhone settings to their defaults.

Keep the iPhone updated to the latest iOS always and never Jailbreak. That's it.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware *** unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed them on your device or/and have Jailbroken. 

It (Hacking) also depends on how careful you are in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password, etc with your friends and family members.

Be judicious when sharing the device's sensitive and valuable information with friends and family members.

**The primary reason for this is Sandboxing. All third-party apps are “sandboxed”, so they are restricted from accessing files stored by other apps or from making changes to the device. Sandboxing is designed to prevent apps from gathering or modifying information stored by other apps.

Security of runtime process in iOS and iPadOS - Apple Support

The sandbox on an iPhone is a security feature that creates a restricted environment for each app to run in isolation from other apps and the operating system. It is a core component of iOS's security architecture and plays a crucial role in making iPhones more secure.

If you doubt the authenticity of the information provided earlier, you have two alternatives:

1. Report the incident to local law enforcement authorities and actively pursue the case.
2. Accept the credibility of the information; it is impervious to hacking. Just as some individuals hold unconventional beliefs, such as a flat Earth or moon landing denial, one has the freedom to believe in anything. The choice ultimately rests with you in this open and free world.