Someone accessing mic, screen view and speakers? How is this even possible?

• Open the Control Center when you see the orange dot and either post a screenshot or let us know what app is showing there.
• There are certainly screen sharing apps including Zoom, Messages, and FaceTime to name a few, but access to your screen would first have to be approved by you first on your device. It cannot be remotely approved.
• Passwords are not visible in your iCloud account, so cannot be remotely changed. Setting up a new device where those Passwords could be seen would require both the Apple Account Password and the Passcode to your device to remove the encryption before they could be synced.
• Not sure what you mean by a new account set up remotely. Your current account can only be removed from your device with physical access and the Password to the Apple Account. If you are seeing a new account signed into your device, then your neighbor knows your Passcode to unlock it and that should be changed.
• Make sure you are using Two Factor Authentication with a known Trusted Phone number.
• I would recommend to review use Safety Check to view the other devices logged into your account and also to review the Trusted Phone number on your account. It is also useful to see what apps have access to your Microphone and any data being shared to others. One thing to be aware of when using Safety Check is if you have deleted any of the apps used to check for shared data, such as Home or Health, then the check mail fail saying it is unable to gather sharing data.

Safety Check for an iPhone with iOS 16 or later - Apple Support

Even if they managed to guess your iCloud password, your device cannot be controlled remotely. Change your password and enable two-factor authentication.

This really doesn’t sound like a real “hack.” Stuff like AirPlay, Bluetooth auto-connect, SharePlay, or Accessibility can make it seem spooky, and the orange dot just means some app used the mic recently, not that someone’s listening live. Remotely controlling an iPhone like that, especially after resets and password changes, is basically unheard of.

If you think it's some more sinister and want to check, run a scan with something like Certo AntiSpy or MVT.