I am setting up a computer which I received from a friend. The options for Windows Update are greyed and I can, therefore, not modify them. I guess this was made by the administrator of the previous owner so that Windows Update would run as he wished. However, the choices he made are not convenient for me. How do I ungrey the options ?

you'll have to ask your friend for the admin details so you can alter them

Have you checked to see if the (Automatic) Update Service is enabled/running?

Services = Start, All Programs, Accessories, System Tools