I had the job in 1996, shortly before retiring from Fire Research in 1997, of looking at fire safety in such play areas. Three of us had some interesting experiences visiting half-a-dozen play areas in Herts. A report was made to the then DoE's Building Regs Division.
There was good guidence on safety, including fire matters, in "Safety in Indoor Adventure Play Areas" by N Balmforth, published in 1995 by the Institute of Leisure and Amenity Management, National Playing Fields Association and RoSPA. It is possible this has been revised or superceded by now.
The principle fire safety recommendations were:
Staff to be well-trained in speedy evacuation from 'Top down'
Parents to be clearly informed of where to meet their children outside the building in the event of an evacuation.
Minimise sources of ignition in the play area.
Ensure kitchens and cafe areas are separated from the play area by fire resistant divisions.
Regarding the mix of ages, most play areas have a separate area for the toddlers (0-3years) where parents can actually stay with the kids. An alternative used by the smaller play areas is to have set periods where the small children can go into the area, again with their parents.