Admin rights for a standard user in OS X I want to create a user with OS X restrictions (Parental Control), which would still be allowed to install applications in the standard Applications folder using its password.

Is it possible? How should I do it?
I wouldn't recommend that you try to put in such a scheme. If you wish to use restrictions, you would generally not want the restricted user to install any application either (for security reasons).

Normally, a non-admin user cannot install applications in the system applications folder at /Applications since it's owned by user root and group admin. However, a non-admin user can install applications under the home directories (~/Applications), but those applications would be available only to that specific user (certain applications that are designed to be in /Applications or those using installer packages to write into system locations may not work well in such a case).

If you wish to allow a non-admin user to install applications into /Applications, then you can add that user to the admin group from Terminal.app (instead of going to System Preferences and allowing the user to be an administrator). Keep in mind that a user who can install applications into /Applications can also remove applications from there (intentionally or unintentionally).