I don't have kids so haven't taken any on flights. However, I've been on a few flights in CW and F with kids about your age on board. Best thing I've seen is coming prepared with things like toys, iPad, etc, rather than relying on IFE on board. One small piece of feedback I would give is that if any games she has on an iPad or other device have sounds, be sure to turn it to silent. That is a bit irritating for those around (and she might not notice if engrossed in Angry Birds level 51...).

With regard to food, you might get lucky and there are options she'll like but (going out at least) you might be better heading to one of the sushi places at LHR which aren't bad. Buying some as take-out to bring on board is perfectly fine too.

Spa treatments are for over 18s only according to the website. This is understandable - if I were a massage therapist I'd feel pretty weird giving a massage to a child. Crosses a line.

You can enjoy the Concorde Room when transferring back. If your daughter likes a burger then get that. The F lounge options aren't bad.

Haven't seen children-sized PJs but hopefully someone will confirm. One of the funny things I do recall seeing on board was a kid aged about 5 or 6 wearing adult-sized PJs

Ignore the unhelpful threads . Some of the most irritating people I've had the mis-pleasure of sharing a cabin with were fully grown adults. However you cut it, wherever you are on a commercial airliner, it's still public transport.