iPhone Apps in Waiting mode for the last 4 days
The springboard has several mechanisms to prevent this from being a permanent situation, but sometimes it falls down. Normally you can cancel a download cleanly. I generally follow this advice to "help" the springboard finish or abort the download transaction:
- (just use the X to cancel the download) - How can I cancel an app installation on the iPhone?
- (reboot the phone) - Why are my updating iPhone apps "waiting..." forever?
- (reboot with airplane mode and sync) - How to fix apps "waiting.." forever after sync?
However, you could have your springboard stuck and a restore is needed. This is discussed here:
- (last ditch efforts and restore as new) - How can I remove this half-downloaded app from my iPhone?
With the information you provided, it's difficult to tell which of the two causes is happening on your phone.
After a week with Apple Customer Support, we resolved the issue by reinstalling iOS with a factory restore, setting up as a new device, then restoring the phone from a backup.
To clarify, a factory restore is not the same as erasing all content and settings. A factory restore can only be done by connecting to iTunes.
Restore your iPhone, iPad, or iPod to factory settings
A factory restore erases the information and settings on your iPhone, iPad, or iPod and installs the latest version of iOS or iPod software.
Get your device ready
Check that you have the latest version of iTunes on your Mac or PC.
If you want to save the information on your iPhone, iPad, or iPod, make a backup.
Go to Settings > [your name] > iCloud, then turn off Find My iPhone. For an unresponsive device or one that won't turn on, learn what to do. If you forgot your passcode, get help.
Restore your device to factory settings
Open iTunes on your Mac or PC.
Connect your iPhone, iPad, or iPod to your computer with the cable that came with your device.
If a message asks for your device passcode or to Trust This Computer, follow the onscreen steps. If you forgot your passcode, get help.
Select your iPhone, iPad, or iPod when it appears in iTunes. For an unresponsive device or one that won't turn on, learn what to do. Or get help if your device doesn't appear in iTunes.
In the Summary panel, click Restore [device].
Click Restore again to confirm. Then iTunes erases your device and installs the latest iOS or iPod software.
After your device restores to factory settings, it restarts. Now you can set it up as new.
Extra notes:
- If you want to preserve Health and Activity data when making an iTunes backup, you will need to encrypt your backup.
- During the new device setup, make sure to select Set Up Manually when prompted for Quick Start. You should not restore from another iOS 11 device.
- After setting your phone up as a new device, you may want to make sure you can download apps on your fresh device before restoring from your backup.