Preview is part of the OS, so you'd have to use recovery to reinstall the entire OS - it will not erase your files; however, it is always best to have a backup first.
Can you check two things: open Activity Monitor (in Applications > Utilities) and if Preview is running, kill the process. And, go to your user library > Preferences and find these:
com.apple.Preview.LSSharedFileList.plist
com.apple.Preview.plist
com.apple.Preview.SandboxedPersistentURLs.LSSharedFileList.plist
Move them to the trash (do not empty yet). Restart Mac and see if the problem persists. The prefs files will be regenerating themselves. If something does not, simply move them back from the trash.