The main user account is fine, but one of the other user accounts has lost all applications...
Can you open the Applications folder when logged in as the affected user? For example, press the key combination shift-command-A in the Finder. If it does open, can you launch applications by double-clicking?
This issue may be a corruption in the accounts database that associated accounts with groups that provide proper access permissions to system resources (including applications and settings). Therefore, one option is to try removing the account and recreate it so the system has a new entry for it with fresh group associations.
In doing this you can keep all the data and settings for the account so they are re-used when you recreate it. To do this, go to the "Users & Groups" system preferences, authenticate, and then select the account and click the minus button. When prompted for what to do with the account's files, select the second option to not change it and keep the home folder as-is within the Users folder.
When the account is removed, click the plus button to recreate it and if you use the same short username as the home folder then you will be prompted to use the existing home folder for the new account. Do this and see if the recreated account now has proper access to system resources.