We flew BA in May. My children were 2 and 4. They allocate seats to families at least three days prior to your flight and try to seat everyone together. Families then get priority boarding so you can get settled. You can order a kids meal prior to flying.
The kids got a kids pack which was a drawstring backpack containing a booklet with stickers, colouring etc and crayons - nothing amazing. They also have a Cbeebies channel on the IFE which came in useful.
Hope this helps.