Yes if you are on Facebook you can go onto The Sims Social.
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The Sims 3 is not free, but there are apps like Shazam, Facebook, TweetDeck, and some games and other apps that are.
Unfourtunatley there is no such thing as Sims Online because The Sims requires a download and in order to download it you'd have to purchase it from a store because it also requires a CD & a bar code. Any "free download" of the Sims would be illegal.
I dono if you can get more mature than The Sims to be honest! But there is a site that lists all the games like The Sims and directs you to where you need to be to play them. All of them are free to play. I will post the link! Hope this helps.
There are plenty of games that are free and safe for kids to play online. A few web sites that specialize in kids games are gamehouse.com, safekidgames.com, and webpaws.com.
Equiverse..org is good.