The foam alone will not ruin a lawn.  The foam does have a different pH that will change a pool's pH, but typically it will help clean the pool.  The amount of water and the wear of kids walking on the grass can cause some muddy spots.  Typically the grass will perk up within a day after the event. But if the event is over one hour it might be best to move the foam to another area.

Yes, it isn’t too slippery and the kids have a blast.

The kids will get wet from the foam.  Bathing suits or a set of clothes that can get wet.  Shoes can be worn, but they will become wet.