My iphone 13 is stuck with remove app dialogue in lock screen. Delete app, Remove from home screen and Cancel button does not work. My phone is getting notifications anad all but, the dialogiue box does not dissapear. What should I do?

Try the Force Restart of your iPhone by using the steps below. It will take a couple of attempts to get the speed and sequence correct and the last step of holding the side button until the Apple logo appears could take up to 20 seconds. Ignore anything else that comes up on the screen until the Apple logo comes up.

Force restart iPhone - Apple Support

Sometimes, a simple restart can resolve temporary software glitches. Turn off your iPhone, wait for a few seconds, and then turn it back on.

1. Restart the device. That's it.
2. Still not solved --> Force restart iPhone - Apple Support

If you still need help, reset your Face ID, then set it up again. Go to Settings, tap Face ID & Passcode, then tap Reset Face ID. Next, tap Set up Face ID to set it up again.

If Face ID isn't working on your iPhone or iPad Pro

Parts and service history

With iPhone 12 models and later using iOS 15.2 and later, you can go to Settings > General > About to see the parts and service history of your iPhone and you can see if the camera has been replaced. If the repair was done using genuine Apple parts and processes, you will see "Genuine Apple Part" next to Camera.

• You will see an Unknown Part  message if the camera installation is incomplete or if the camera:
• Was replaced with a nongenuine camera
• Was already used or installed in another iPhone
• Isn't functioning as expected

This message doesn't affect your ability to use your iPhone or access your camera.

Learn more about iPhone parts and service history.

If your iPhone's camera has been previously replaced, repaired, or serviced by an unauthorized service provider, it's worth noting that Apple may decline to provide service for your device. The decision to refuse service will depend on the specific components that were affected by the unauthorized service.

Get a Genius Bar Reservation and Apple Support Options - Apple

Contact Genius Bar.

Manage Reservations - My Reservations - Apple

Passcode

Your data is not lost if you have a backup either on iCloud or iTunes.

If you see an iPhone or iPad unavailable message or a "Security Lockout" screen

If you forgot your passcode, you can use your Apple ID and password to erase and reset your device without a computer.

Learn what to do if you see "[Device] unavailable" or "Security Lockout" on your iPhone or iPad.)

iPhone is disabled.

Following this process is the only way out if your iPhone is disabled. The steps given in this link will help you reset the passcode -> If you forgot the passcode for your iPhone, iPad, or iPod touch, or your ...

Regarding your data…

1. If you have an iCloud or iTunes latest backup, then there is nothing to worry about. If not read more...
2. You have synced your data to iCloud, then what you will get back is what you have synced to iCloud and uploaded to iCloud Drive; the information that is synced and stored in iCloud are, Contacts, Calendars, Bookmarks, Mail, Notes, Voice Memos, shared photos, iCloud Photos*, Health data, call history, and files you store in iCloud Drive. (*-If you have turned on iCloud Photos, your content is automatically stored in iCloud.)
3. You have imported your Photos and videos to Mac/PC then they are safely residing there on Mac/PC
4. You have uploaded some of it to Cloud Drives using the Files app (iCloud Drive, Google Drive, OneDrive, DropBox, Flickr, box, AmazonDrive, Adobe Creative Cloud, etc). The data remains there.
5. If you have not backed up or do not have the latest backup, nor imported nor you have synced or uploaded your data to cloud drives prior to the situation that you are in, then I am sorry, all your data is lost.

Password

Apple ID and Activation Lock

iCloud uses Apple ID credentials.

If you do not remember the Apple ID Password then follow the steps given in this Apple Article -> If you forgot your Apple ID password - Apple Support

If you do not remember the Apple ID then follow the steps given in this Apple Article -> If you forgot your Apple ID - Apple Support

If you are the owner or the owner has shared all information with you then to open Activation Lock:- If it is Activation locked, read here --> Turn off Activation Lock - Apple Support Activation Lock for iPhone, iPad, and iPod touch - Apple Support

Learn how to remove a device from a previous owner's account.

If you are not the owner and do not have the Apple ID and Password then there is no way that you can get into this iPhone unless the original owner shares the Apple ID and password with you. If you are lucky you can get into this iPhone if they (owner) accidentally remove the device from their Apple ID.