You can book a cash ticket for anyone.

If you have a HHA, you can book for anyone using Avios but only if they are part of the HHA or on your Friends and Family list (which can only be changed once per 6 months). Sounds like that's not an option for you.

If you book a cash ticket for someone else, no you can't get the Avios and TPs. They are for the person flying only.

Hope that's some help.