Which operating system? First suggestion (although from your other problems not likely), scroll down to the bottom of the parts panel window. Sometimes search appears at the bottom of the list (and is thus hidden as there are more bins than slots in the window.) Given other parts problems this isn’t likely though. Typically search problems (which there haven’t been any of for several years) were caused by Windows10 early patches (a forum search for missing search should turn up the old threads which may be worth reading.) and otherwise by file permissions not allowing writes to bin files. I would be tempted to delete the Fritzing installation, and the user directories (which won’t be changed during an installation) and reinstall as a first step to see if that fixes the issue. The user directories location varies by operating system:
There are two user directories (with your parts and the parts database) which don’t get touched during an install (to not affect your sketches during upgrades). On Windows they a)re in
c:\users\username\AppData\Fritzing\roaming\Fritzing (which is a hidden directory so you need to enable hidden directories in explorer) and
c:\Users\username\My Documents\Fritzing (where username is your windows id)
If you don’t have any parts or sketches you want to keep you can just delete those two directories and Fritzing will recreate them, or you can move them aside by renaming them if you wan to keep something in them.
linux
~/Documents/Fritzing/parts
~/.config/Fritzing
Mac
/Users/username/Documents/Fritzing/parts
~/.config/Fritzing
The usual reason for search and parts problems is file permissions (Fritzing is bad about reporting unwritable files). Fritzing is intended to be installed as the user running it (i.e. not as root on a Unix system, but as your standard user without sudo.)
Peter