There are plenty of apps that kids can use without parents having to worry about it. The best kids apps for android according to Android Authority website are:
ABC Kids: (Free) – An educational app focusing primarily on phonics, learning the alphabet, and a little bit of writing.
Amazon Free Time (Free / Varies): It boasts a collection of over 10,000 children’s books, TV shows, movies, and other content.
ColorMe (Free with in-app purchases) – ColorMe is one the most popular coloring book apps available suitable for both kids and adults.
Duolingo (Free): it is an educational app for language learning and features a bunch of languages, including Spanish, French, German, Ukrainian, Hebrew, and over a dozen others.
Google Play Books (Free -books cost money): Arguably the best of the kids, it has a large selection of both adult and child content.
Intellijoy kids (varies): Another other app for reading, counting, shapes, music, animals, puzzles, preschool, and a lot more.
Kids Doodle (Free): it is a drawing and coloring application where Children can draw and color whatever they want, save it for later, and even create slideshows with their drawings.
YouTube Kids (Free/$9.99 per month): An effort by Google to separate the kid friendly content on YouTube and then put that content in its own application. YouTube Kids is a good resource for parents and there are a ton of videos available for kids to watch.