"I am unable to play You Tube videos since upgrading to OS 10.13.4"
You may have a third party Safari extension or plug-in installed that's causing a conflict when the routine update was installed.
Troubleshooting help here > If Safari is slow, stops responding, quits unexpectedly, or has other issues - Apple Support
"Since upgrade to the new OS10, the search function on the mail at the top of the screen disappears after it is used once. Requires shut down and then restart"
A Safe Mode boot deletes system caches that can help after updating or upgrading macOS.
To start up in safe mode:
- Start or restart your Mac, then immediately press and hold the Shift key. The white Apple logo appears on your display. If you don't see the Apple logo, learn what to do.
- Release the shift key when you see the login window. If your startup disk is encrypted with FileVault, you might be asked to log in twice: once to unlock the startup disk, and again to log in to the Finder.
To leave safe mode, restart your Mac without pressing any keys during startup.
Then try Mail.
Use safe mode to isolate issues with your Mac - Apple Support