While on holiday I'm playing Hero's of Incredible Tails on my phone along with my kids on their tablets. It's a free slash em up with a touch of grindy MMO splash. Free to play, but very heavy on pay 2 progress faster items.
As it's mobile gaming only, there is no keyboard. Which does mean there is no or very little chat which makes it very child safe IMHO.
http://hitmobile.nexon.com
On droid and apple. I found a way to install it on my kids Amazon fire for kids without rooting them which was challenge as its integrated into Google play services.
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