Yes, she can and should use the Concorde Room. The only showers, I'm afraid, are in the Galleries (Business) lounge. They are adequate, but you do have to work your way around construction works through the crowds to get there. Still, it's good to see how most people have to travel so you appreciate F more
For security, use the left side of the terminal (as you enter) where there is a First/premium security line. She should show an F boarding pass and she is likely to be escorted to the front of the line.
Phone the You First line at BA to book a spa appointment, you can try (but may well not succeed) to book from about a month ahead. It seems not, see below.