By virtue of departing in First, you're entitled to use any of the T5 airside lounges, including the CCR. The only thing that your relatively early departure rules out (from a common-sense standpoint) is reserving a cabana, as they are only available at 08:00. The CCR, the Elemis spa and the other lounges open much earlier than that.

Breakfast in the CCR is in a sit-down area, with waiter service. The food is pretty good, not 3* Michelin, not that bad either.

The night before your TATL flight, assuming your MUC-LHR is on BA Club Europe, you will arrive at T5. As suggested above, as you enter the Arrivals hall, you can stop at the Marks & Spencer store to pick up provisions before heading over to the Sofitel, if you just want snacks or drinks rather than a full meal. If desired, you can use the free rolling luggage carts through the connecting tunnel, all the way to the hotel threshold.

The morning of departure, when you re-enter the T5 departures hall, make your way to the far right of the check-in desks, to the dedicated First check-in area. You will then clear security via the "fast"-track line; as soon as you are through the checkpoint, look immediately right for the double white doors, which is the not-so-secret "secret" entrance to the CCR.